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TABLES
DE SINUS.
TANGENTES,
ET SECHANTES:
E T D E
LOGARITHMES
DES SINVS, TANGENTES,
& des Notnbtes depuis Tunicé
jufques à loooo.
%^vee une Méthode dcHfiudre trei-facilement
far Uurmyen tous lei trianglei ^ ReBili^
gnei é' Spheriques , é" plttjfeurs c^ftimi
AjlrotHmicjites.
■ Par A. V_L A C Qj_AJy('aft-/i
Detniete Edition, conigée & augmentée.
• »
rV ^ L r O 2^,
■^ Ch« lEAN THIOLY , rue Merdcw
à la Palme.
[y%'^
« ^
/¥**
M. X>C. L X X.
AVEC TRIVILECE DY ROT^
m
J
1/
8
il** I,^^P.I:ii.iîiS.'" '
1
4 Ch A r . L D^ f^f^g^ ^ ces TMes.
Voulant calculer par nombres vulgaires^ il faut
mulriplier le (econd nombre parle croi/iéme > 8c
divifer le produit par le premier : le quotient fera
le quatrième.
Mais , fi on veut calculer par leurs Logarith-
mes^ il faut ajouter le Logarithme du fécond avec
le Logarithme du troifiéme , &ôterdelafomme
le Logarithme du premier : le nombre rcftant fera
le Logarithme du quatrième > lequel étant cher-
ché dans la première ou dernière Table ( félon *
qu'en fera la nature ) donnera le quatrième re-
quis.
Cette manière eft beaucoup plus facile que
Tautre ^ principalement aux refbfutions de tous
les Triangles Sphcriques > car aux refolutions de
plufieurs Triangles rcftilignes % comme de la 3 .
4. 6. Prop. &c, il eft plus aisé d^ûfer de l'autre
manière > ce que je lailie à la difcrecion des cal-
culcurs.
Or dautant que la dernière Table contient
feulement les Logarithmes des nombres dépuis
l'unité jufques à xoooo> je montreray comment
on pourra trouver le Logarithme d'un nombre qui
fera entre 10000 & iogooooo>& au contraire.
,^i. O^crchez dans la dernière Table le Lo-
garithme des quatre premières figures du nom-
Brç.donné.
1. Ocez le Logarithme trouvé du Logarithipc
immédiatement fuivanc en la Table j pour avoir
leur diftcrence.
3 . Multipliez la différence trouvée, par les figu-
res reliantes du nombre dbnnéj& coupez du pro-
duit
\-
Ch a p. 1. D^ l^^fi*g^ ^^ ^^^ Tables. 5
duic vers la main droite autant de figures que font
reftécs.
4. Ajoutez le refte du produit au Logarithme
premièrement trouvé,la fomme fera le Logarith-
me requis , fi on change la première figure , la-
quelle doit toujours être moindre d'une unité que
le nombre des figures ^ dont le nombre entier
donné confiftc. \
EXEMPLE. Qu'il faille trouver le Loga-
rithme de 3 567894.Premicremét je trouve le Lo-
garithme de 3567, qui eft 5. 5^13031 : lequel
étant ôté de 5.55 24248 , la différence fe trouve
1 2173 laquelle étant multipliée par 8^4 (les trois
figures reftantes , ) le produit eft 1 087598 , dont
crois figures étans coupées> refte i o87>qui étans
ajoutées au Logarithme 3.5523031, la fbmme
eft 3 . 5 5241 1 8. Enfin la première figure 3, étant
changée en 6 3 le Logarithme du nombre donné
3567894 eft 5.5524118. ,
Ainfi le Logarithme de 1 2 5 6oj eft 5 .0990 1 3 7:
^dç 2358oo«> le Logarithme eft 6.3725454.
NOTEZ.
?tfr|P4 . ^.. ^ ^ tf7t94
00000
Etant donné le nombre iT^~ '• ou 3 y 7
^^iS^rrià'^^* ^^w" Logarithmes font les mê-
mes du nombre entie*r"3 567894, horfmis la pre-
mière figure , fçavoir o. j 5 241 18 : i . 5 5 241 1 8.
2.55 24118, &c. & pour les trouver il n'y a au-
cune différence.
Et fi un nombre entier avec une fraélion déci-
male , n'ayant en tout plus de 4 figures, eft donnç,
on trouvera fon Logarithme cxadement dans 4a
a 3 même
$ Ch A r . I. D^ l^^f^^ ^^ ^^^ tables,
mcmc Table. Comme de ^^st; > ou JJt^,, ou
3 j 67; , les Logarithmes fc trouvent vis à vis
le nombre entier J567 >. en changeant feule-
ment la première figure y comme il z' écé dit
cy-defliis.
Mais 3 fi une autre efpece de fraâion cft jointe
à un nombre entier , reduifez ce nombre là à une
^radkion impropre , & ôtez le Logarithme du Dé-
nominateur du Logarithme du Numérateur^ le re-
fte eft le Logarithme requis.
Comme 3 ^ ccant réduit , vient -^ > donc
G. 6010690 { le Logarithme de 4J étant ôte de
I. 17^0913 ( le Logarithme de 15 > ) le rcfte
0.574051; eft le Logarithme de j j- ou 3 7^.
Vous voyez donc :cy que les fractions décima**
leSjtant en l'ufage des Logarithm^s^qu en 1 ufage
des nombres vulgaire$>donncnt une grandefacili- -
té : & partant nous les recommandons par deiliis
toutes les autres*
Pour trouver le Logarithme d un nombre rom-
pu » il faut ôter le Logarithme du Numérateur du
Logarithme du Dénominateur , le rcfte eft le Lo-
'rithm. requis j en luy ajoutant la marque - , qui
ignifie moins.
Mais> il faut fçavoir qu'on jdoit opérer autre-
ment par Logarithmes des nombres rompus que
par Logarithmes des Nombres entiers 5 ou d'ea-
ciers avec fraûions > ce que nous n enfeignerons
pas icy > parce que rarement viennent-ils en ufà-
gç es refblutions des Tringles. Ceux qui le défi-
rent fçavoir, le pourront apprendre tnl^jinthme^
tique JLéOgmthmerique àHimy Briggsi où le fonde-
ment
Ch A P . L *D^ ^^frg^ àe ces tahles. 7
ment & lexccllenc ufage des Logai^ichmes es
queftions Arichmeciques Se Géométriques font
amplement déclarez*
Trouver le nombre dm logmthme donné.
Cherchez en la dernière Table entre les Loga-
rithmes de 1 000 Se loooo i ( n'ayant égard à la
première figure J le Logarithme donné>& remar-
quez ces deux chofès.
Premièrement » fî vous trouvez exaâement le
Logarithme donné > vous y avez vis à vis le nom-
bre requis : Et fi la première figure du Logarith-
me donné eft moindre que 5 3 coupez du nombre
trouvé' vers la droite autant de figures qu'elle eft
moindre » le refte fera le nombre entfer requis^ ôc
les figures coupées feront des fraâions décima-
les. Mais 5 fi la première figure efl plus grande
que ^ , augmentez le nombre trouvé d'autant de
zéro qu'elle eft plus grande. Ainfi le Logarithme
j. 5523057 étant proposé j Ton nombre fera
}j67 :fî 2.y5i}oji, ion nombre fera 55(^7^ : fi
1.5 5 23 0} I , fon nombre fera j 577;:fi o. 5525031
fon nombre fera 3 -^ : fi 4.5 5 1 3 o 3 1 /on nombre
fera 55670 : fi 5. 55250511 fon nombre fera
55(9700. Ainfi des autres.
Secondement > fi on ne trouve pas exaâemenf
le Logarithme donné y & qu'on demande plus de
quatre figures, faites ainfi.
I. Cherchez comme devant f n'ayant égard à
la première figure } le Logarithme prochainement
moi&dre que le donné > & prenez le nombre ré-
a 4 . pondant
s Ch A. p . I. P^ ^ «îA?^ àe ces TMa.
pondant an Logarithme trouve pour les quatre
premières figures du nombre requis.
, 2. Otcz le Logarithme trouvé du Logarithme
donné , & augmentez le rcfte d'un , deux , ou trois
zéro, félon le nombre des figures que vous deman-
derez outre les quatre trouvées.
3. Divifcz ce refte airtfi augmenté par la dif-
férence çnrre le Logarithme trouvé & cçluy qui
le luit imxTiediaûemcnt , & mettez le quotient
vers la droite des quatre trouvées. Cela fait re-
gardez la première figure du Logarithme donnéji
laquelle montrera le nombre çntier & la fra-
tftion du nombre 'trouvé , comme nous ayons dit
auparavant.
EXEMPLE, Qu^il feille trouver le npnibrc
répondant au Logarithme donné 4.5 5 24 1 1 8.
Le Logarithme qui fe trouve c(i la Table entre
ceux de 10003 & lopoo (fans avoir égard à*la
première figurej) approchant le plus prés & moin-
dre que le donn4> eft 3.55230}!, duquel le nom-
bre eft 35^7> qui font les quatre premières figu-
res du nombre requis. Or ce Logarithme trouvé
iCtant ôté du donné y Iç rçftç çft ^ 1 08 7 , que vous
augmenterez de trois zeroj, pour avoir 1087000-
Divifcz cecy par 1 2 1 7 ( la différence entre le Lo-
garithme trouvé & le fiiivant , ^ le quotient eft
8p 4 : mettez ces figures après j 5 ^7 > & vous au-.
rez le nombre 3 $167 Sç^. Or puifque la première
figure du Logarithme donné eft 4 , le nombre re^
^uis eft 3 Ji 6787^1,
Tr^ftver
Chap.I. De Cufage de CCS tables. 5
Tromjer la Kactnt c^arrée m Cubique £un mmh
bre donné.
Bien que mon intention ne foit que de bricvc-
ment d'écrire en ce lieu U manière de fupputec
Icis Triangles : Toutesfois puifque l*ufage des Lo-
garithmes eft admirable es extractions de Raci-
nes Quarçcs , Cubiques , &c. j*ay trouvé bon d'y
ajoâcer en peu de lignes > comment on les peut
trcs-facilement extraire.
Tour avoir la Racine quarréc Sun nombre donnée
prenez» la moitié du Logarithme du nombre
dmné , laqueUefera le Logarithme de la ra*
cine c[uarrée quon demande.
Comme fi on demande la Racine quarrcc dcr
1257 : foi^ Logarithme eft 3.05^93 3 5 3*& la moi-
tié I. S,^966j6 y laquelle eftle Logarithme de
3 5 —^ la Racine Quarrée rcquifè.
tour troufver la Racine Cubique d^un nombre
prof osé , le tiers du Logarithme du nombre
donné fera le Logarithme de la Racine Cu^
bique quon demande.
Par exemple on demande la Racine Cubique
de 11570. Son Logarithme eft 4. 099335JJ& le
fiers 1 . 3 6(j 445 1 , qui eft le Logarithme de 1 37^
la Racine Cubique requife.
S 5 1)0
le Ch A p . I. D^ l'^frg^ ^^ cet Tables,
De la nature et conflrnSlim des Logarithmes.
Les Logarithmes font à^s nombres pris à dif-
erecion » lefquels étans joints oucoirefpondans
à des nombres Géométriquement proportionaux
retiennent toujours entre eux des différences éga-
lés $ ou bien qui gardent la progreffion Arichmç*-
tique y Candis que ceux defquels ils font dits Le*
garithracs , confervent la Géométrique.
Voyez la première colomne de
la Table ftiiuante > ou font les
nombres Géométriquement pro-
^rcionaux > aufquels répondent
vis à vis dans les autres colom-
iies leurs Logarithmes > qui peu-
vent dtre pris à difcretion > com-
me vous voyez ^ étant libre de
pofer ce que l'on veut pour pre-
mier Logarithme , & pour leur
différence progreflîue.Mais>ayanc
déterminé le Logarithme de deux "
nombres , il n'eft plus libre d*en déterminer d'au-
tres. Par exemple le Logarithme dr lunicé étant
1 , & de 2 , étant t , le Logarithme de 4 fera par
neccflîté 3 > & 4 fera le Logarithme de 8. Que fi le
Logarithme de lunité eft 5 > & le Logarithme de
i>eft 5 , le Logarithme de 4 fera ncceuairement y 3
& 9 fera le Logarithme de S.Ainfides autres.
OrJa propriété des Logarithmes eft telle , que
quand quatre nombres font proportionaux j
la fomme de leurs Logarithmes extrêmes eft éga-.
le à la fomme des Logarithii;ie$ moyens.
EXEM
pfp-
tUrarié' 1
fort. 1 mes. , j
I
I
3
2
X;
s
10
4
3
7
10
8
4
9
3<>
16
S II
40
3^
6
13
5^0
M
7
If
^0
\%%
S
17
70
^^6^ 9
IP
80
fiilio
zl
90
1024
h'
13
lOO
CuAV.l.Ve Vufàge de ces tables. 1 1
EXEMPLE. CommeicftàS^ainfii^cft
à 64* la fomme du Loganchme de 1 > & du Loga-
rithme de ô^ikx2L égale à la fomme des Logarich«
mes de 8 & de 1 6.
D*oii vient qu'au lieu de faire la Règle de croi$
par multiplication & diui£on> pour trouver corn*
me à Tordinairç le quatrième nombre proportio-
nel > il on ajoute les Logarithmes des moyens» &
de leur fomme on ôte le Logarithme du premier>il
reftera le Logarithme du quatrième requis , à Coti
duquel on trouvera ledit quatrième nombre.
Et partant il n'y a qu'à faire des Tables defdits
Logarithmes correfpondans à tous les nombres
naturels» comme je montreray cy-aprés. le dy cor-
refpondans dépuis runité cohlecutivement (ans
laiiFer de vuide y comme il y a entre les nombres
cy-defTus proportionaux 4.8. 16. &c. oià les nonv-
bres }.f «y.p.&c. manquent ^ qui pourtant doivent
avoir leurs Logarithmes , parce qu'on en peuc
avoir bcfoin. C eft pourquoy > il faut faire la diffe-
tence defdits Logarithmes Ç\ grande > qu'on
puiflc aisément affigner à chaque nombre fbn
'Ti^U^.GemALoganth^ ' Logarithme, fans que les fra^
Trop.
mes.
I
10
lOQ
1000
lOOOO
I 00000
1000000
10000000
ioooooooo ( 8.0000000
0.0000000
1.0000000
1. 0000000
3.0000000
4.0000000
f.OOOO0OO
é.OOOOOOO
7.0000000
â:ions en puiflent être feniî-
blés, comme il fera dit.
A cette fin on a fupposé
pour plus .grande facilité que
le Logarithme de i. fut o. &
le Logarithme de 10 fuc
uooooooô,le Logarithme de
100 fut i.ooooooo, celuyd^
1000 fut }.booQQQQ>&c ainfi
enfuie
/
1 1 Ch a p . I. D^ tuf âge àe ces Tables.
.cnfuitc> comme vous voyez en cette Table. Où il
cft à remarquer que la première figure du Loga-
rithme ( nommée ordinairemçnt CaraSieriflique )
cft toujours moindre d une unité que les figures
dont le nombre naturel eft composé. Si par exem-
ple il eft de 8 chifres, la première figure de fon Lo-
garithme fera 7. Si de 1 1 chifres^ W Logarithme
aura 1 1 pour CaraBmfti^ue.
Et fur ce pied & fondement on a trouvé les Lo-
garithmes de tous les nombres, même de ceux qui
font de 1 à lo^de 10 à loo^deiocà iooo>&c.doilt
onadrefsé des Tables > fi bien qu'au lieu d opé-
rer par multiplication & divifion pour trouver le
4. nombre requis, fi on opère par Adition & Sou-
traâion des Logarithmes qui répondent aux trois
nombres donnez, on aura le Logarithme du 4.re-
quis , à côté duquel il fe trouvera en la colomne
des nombres naturels.
Et d'autant qu'avec les Tables des Sinus Se
Tangentes, comme étans des nombres naturels,
il faut opérer par multiplication & divifion , on
a auilî cherché les Logarithmes de tous lefdits
nombres de Sinus & Tangentes au regard du Si-
nus total 1 0000000000, auquel on applique pour
fon Logarithme 10. 9000000, &c tous les autres à
proportion,que Ton a fubftitué en la place defdits
Sinus & Tangentes ordinaires.
De façon qu'au lieu de les multiplier & divifer
s'ils y ctoient , on ne fait qu'ajouter & foiitrairc
leurs Logarithmes, pour avoir le 4.requis , à côte
duquel on trouve le degré & minute , comme iî
c'étoit le Sinus ou Tangente même > puis-
qu'ils
>
A
C
B
6
D
C
B
E
D
B
F
£
"i
G
F
G
H
F
G
1
H
I
K
H
Pfêport,
— — *
I.OOOOOOO
3.6121777
10.0000000
10.0000000
5^.6134131
3,1611777
ro.ooooboo
7.498^411
j^ .61341 31
togarit.
o.oooooooo
0.3:0000000
I.OOOOOOOO
1.00000000
0.7JOOOOOO
0.^0000000
l
Ch A p . I. De Cufâge de ces tAbles, j 3
qu'ils font fubftimçz en leur place.
Poftr trouver le Logarithme d'un nombre donné
quel qu il /bit y comme f4T exemple de p, qui efl entre
I ^ I o > de/^uels les Logarithmes /ont déjà donne:^
fcavoir o. jooçoooo y & i» 0000000 » oh bien
D.OQOOOooo, & i. oooooôob, les augmentant àwt
Kjero y pour trouver plus exaSemem le Logarithme j
faites en cette forte*
Entre i & 10 au-
gmentez d'autant de zé-
ro que le Logarithme de
îo & des autres propor-
tioriels , comme icy de
fept, pour avoir exa(5te-
ment dans le même
nombre de figures le Lo-
garithme yequis^fç avoir
entre les nombres A ^ B>
trouvez un moyen Geo*
métrique proportionel
C \ lequel étant moin-
dre que 9. 00 000 00 >
il faudra chercher en*
tre-le moindre C > &
le plus grand B un au-
tre moyen proportionel
D> qui efl; encore moin-
dre que 5?.oooooo03c'efl:
pourquoy entre le mojn-
dre.D & le plus grand B
on cherchera un autre
mojen proportionel E
10.0000000
8.6^^6431
7.4985^11
10.0000000
P.3OJ7IO4
8.6^^6431
■
^.30^7104
8.97^8713
8.6J9643I
^.3077*04
9.13^8170
I. 00000009
O.87JOOOO9
0.75:000000
1. 00000000
o*P37îocxx>
0.87^00000
r. 00000000
0.96875000
o«937îooo«
0,96875000
0.95311500
0.93750000
0.96875000
0.96093750
8.9768713 }o,933 11500
9.1398170
9.057P777
8.9768713
0.96093750
0.9^703 12. J
0.953 i»f<»
entre
H
K
L
H
T
M
H
T
N
M
N
O
IM
O
P
M
O
Q
Q
R
P
R
S
P
R
T
S
T
V
S
Proport
9.0S79777.
9.0173S33
Lcgttrith.
^-9S 70^11$
o.9SS07^ïz
8,^768713 10.^5:3125:00
O'^ff 07812
0.9S4ÏOIS6
0.5)53125:00
5^.0173333
^^9970796
8.5>7687ï3
*?.oo72oo8 o.^y45'8y84
^'9970796
• — Il ___^^^^
^.0072008
5>.oo2f388
^.9970796
^.0021388
B.99960%^
^•9970796
—
^.0021388
p.0008737
^•9996o%i
p.0008737
^.«002412
8.pP5?6b88
- ■ — ^««^
p.0002412
^'9999lfo
8.pp5)6o88
0.^^4101 f 6
0'9S41^9^
0-^^434170
0.^^4101^6
0-^434170
o.p5'4223éî3
0.^5:4101^6
Ch A P. I. Z)^ tufage de ces Tables.
" entre leqifcl & le plus
grand Ê on trouvera un
quatrième moyen pro-
portipncl F , qui eft icy
encore moind re que
'5^.0000000, c'cft pour-
quoy il faudra trouver
entre \c moindre F,& le
plus grand B , un cin-
quième moyen propor-
tionel G y qui fi^ra icy
prgrâd que j.ooqôooo^
ainiî entre le plus grand
G* & le prochainemenc
moindre F, on cherche-
ra un fîxiémc moyen
proportionel H, qui fe-
ra maintenant moindre
que 9 ooooooo : c'eft
pourqupy cptre ce moin-
dre H , & le prochaine-
ment plus grand G > oh
trouvera un feptiémc
moyen proportionel I ,
o.pr4254if qui eft bien plus grand
o.5?5r4*4éya j que p. ooooooo , mais
^«00024 12
^.0006831
%.9999Z^o
p.000083 1
^.0000041
8.^9Pi?25p
^.0000041
^'99996So
2.9999XSO
0-^434^70
o.p3r4284$7
0.^5412363
0.^428467
0.^5:42 5'4i5:
01^^422363
o.pf4254rsr
0.5^542388^
o.p5'422363
o.5?54»388^
o.p5 424652
o.P5'42427r
0.^42388$
1
0.^424271
o.p5' 424080
0.9^42388*?
non pasr avec un fi grand
cxcez comme le précè-
dent G. Ain/î en cher^
chant entre le prochai-
nement moindre & le
pochainemct plus grâd
des
Ch A p . L D^ Vuf^ge de ces Table$. i y
V
Y
2^
V
z
Y
Frafort. | LogMrit.
p.0000041 ; 0.^2414171.
^'9999^4$ ; 0.^^414117
^»9999éSo 1 0.^5:414080
^.0000041 1 0,^5:414171
%.999994$ 0.^5:414123
2.9999^^$
V
9c
Z
T
AA
&
AA
BB
&
BB
ce
&
BB
ce
^.0000041
2*999999%
2.99999^'i
^.0000041
^.OOOOOI^
2.999999%
9,0000016
^0000004
2.999999i
0.^5:424117-
' ■ .
0.^414171
0.^^414147
0.^^414113
I 1 .1. . . ■ r
o.py 424171
0;5>î4*4iJ^
o.^J4i4»47
»■ ■ ' ■ ■— —
0.8^41415^^
0.^4141^3
0.51^414247
des nvoycns Gcome-
triques proporrionelsj
on aura des nombres
qi|i approcheront toû-
J9urs de plus en plus
du nombre proposé
9. ooooooo> lequel en-
fin fe cencontrera icy
le 16. moyen propor-
cjonel : Après quoy il
fera facile de venir à la
connoifTance de fbn
Logarithme ; car com-
me entre les nombres
A> B> nous avons trou-
vé un moyen Geome-
erique proporttonel C>
fi entreleurs Logarith-
mes on trouve un mo-
yen Arithmeti^e pro-
porcioneli celuy-cy fe-
ra le Logarithme du ■
pKtnîer moyen Gct)metriquc pyopqrrionel C,
C cft de cette manière qu'on trouvera les Loga*
rithmes de tous les autres moyens Géométriques
propottionels > 8c par confequcnt du dernier
^-.^ooeooo > ou du nombre proposé 9 , fçavoit
0^7^4141^. ^
Qn ne trouvera pas autrement les Logarithmes
des nombres premiers , & par l'addition de leurs
Logarithmes on aura facilement les Logarithme»
des auei^es nomfcte^ j ce qui eflr G, évident par ce
que
f.»3000O4
2.999999^
0.^54141^0
2.999999% \ 0.^^414147
^^0000004 0.^^4141.53
5?.ooQoooo 0.515' 414151
2.9999992 0.9s ^%^%s^\
N
16 Ch A r . 1 1. Des TfiangLreStU, reSiangt.
que nous avons die cy-defliis> que j ay^onte d'eiî
parier davantage, le fçay bien plufîeurs autres
Méthodes pour l'invention des Logarithmes ,
mais je n'en fçay point de plus prompte que
celle- cy.
N
- CH APIT RE IL
Du Calcul des Triangles reStUignes reSf angles.
Observations.
ï. *r\Es Triangles redanglcs, tant reâilignçs
JL/quc Spheriques , les cotez comprcnans
Tangle droit font appeliez j^tmbes , & le côte qui
luy eft opposé, hypotenufi.
2. De tout Triangle tant reûiligne que Sphc-
riquc , le plus grand angle eft foûtcnu du plus
grand côté. Et le plus grand coçé foûtient le plus
grand angle.
3. De tout Triangle reâiligtie les trois angles
pris enfemble font égaux à deux droits.
4. Aux propofîtions fuivantes généralement
tioxxs avons obfervé un tel ordre , que les premie-
rs font pour trouver les Angles , & les dtxriierçs
pour les Cotez. Et de ccux-cy aux Triangles re-
âangles ^ premièrement les jambes^ & puis après
î'hypotenufe.
j. Il eft expédient que les tçrmes connus, tant
angles que cotez > foient marquez d*une petite li-
gne.
Ch A p . 1 1. Des TrUngl. reBil. reHangL 1 7
gne, & les ternies requis, d un petit cercle, ou o^
comme on peut voir icy.
I. P R o p. Etans connues les jambes , trouver
les angles aigus.
Comme' une jambe ,
Alàn^e ]mnbe\
Ainfiie Sinus total,
A la TAngemde 1^M£Ù apposé à Nme jambe,
EXEMPLE-AuTrian-
glc rcftanglc A B C *
ctans connues les jam-
bes AB 1124, &BC
606 i trouver l'Angle
A ou C*
■
Par nombres Vfdgairts*
Comme la jambe A B 11^4
A la jambe B C 606
Ainfile Sin. total laooodoo
A la Tangente 5 J5>i 4 j 9 de A 28 d: 26
Et partant C comblement de A 6 1 d: 46
Par Logarkbmcs.
Le Lo^Arithme de A B 11^4 eft i •0597^^3
Le L(^îïrithmc de B C ^06 cft 2.7^247 26
Le Logarithme du Sinus total 10.0000000
Rcâeia Tangente Log^afithmi<iuç p . 7 j 1706} de
A 28 d: 26,
II*PR0]?«
\ 18 C H A P . 1 1. P<?i trUngL reSfil. reSlAngl.
II. Pu op. Etant cônnucM'hypotenufe* & urlo
jambe , trouver les angles aigus.
Comme thypoténufe^
Ah Sinus total j
jiinfi la jambe cçnnuh
Ah Simts de t angle oppesé à cette fomte.
I II. Prop. Etans connus' les angles , & une
jambe, trouver l'autre jambe.
Comme le Sinus total 9
A la jambe connue, r C *^^ conmë,
Ainfi la Tangente de l'angle ^gu adjacent à ta jam^
A la jambe requifc*
|I V. P R o p. Etans connus les angles , & l'hy po-
tenûfe , trouver laquelle on voudra
des jiambes. . ^
Comme le Sinus tot^i
A l'hypotenu/e ;
Ainfi le Sinus de Vaftgh apposé k la jambe reqkifi»
Aid^a^ereifu^e. :
V. Pr o pfEtant connue rhypôteKufc > &'iSnr des
jambcs>tijoovci:rautre jambe.
Ch^cèékfn^efiia^enmarks^aitgles aigus p^ **
Propi EtptOfaprA l^i^imbo r^qmfe parla 5. #» 4*
Auïircmcnç & trcs^fetileHicnt par Lôgariilhttîcs*
Ajouter le Logarithme de la fimme de Phypo^ \
tenufe, & de la jambe, au Logmthmeje leur
/. ' dtf erem^
/^
G tt A ï < 1 1. JÔ^i friaHgt. repiLrepMgL t ^
i^ircnce : U moitié de lafomme de ces Lo^rithmèi
tffi U Log^ithme de U jambe requifi* '
EXEMPLE.AuTrian-
\ gle A B C> écant connue
l'hypotcnufe A G i i 7 7>
& la jambe AB 1114s
on dgatode la - jam^
i'hypotcnuic A G 117:^
f la jambe A B 11 14 Logarithneu
U fomme 2401 *--^ }. 3eo}9li'
JidifFercnGC tj} --"^ ^- 184^5^ '4
la fomme 5.565 08 jô
la moitié de la fomme 1*^8154x8
eft de B G 6o6é
«
V I. P Ro i>. Etahs. cornius les angles j & Uiic jàim
be , trouver Thypotenufc.
Comme le Sinus total à
A là j/arÀBe connue ; (connulli
Ainfi U Sécante de t angle dgH adiaceHt a 14 jmmh
A Vhyjfotenuje.
Si quelqu'un veut connoltre le Logatithitie dé
"ia Sécante d'un arc > on le trouvera en ôtant 1^
Logarithme du Sinus de foh complément , du Lo-^
' garithmc doublé, du Sinus total î le rcftefclraU
Logarithme icquisi
Ainfi ôtanf >i 9445811 le Logâtithihe du Si-^i
nus de 61 d^46.de lOi 0000000^ rcftp 10.05 5417s'
le Logarithmede la Sécante de 1 8 daOi
' J a Atotr«
%o Chat. II. D^i tmngl. tectiL re^angl.
Autrement fans Sécantes*
Comme le Sinus de îangU opposé à la jumio cornue^
A la jambe connue:
jiinfi le Sinus totah
A Chypotenufè.
VIL Pro p. Etans connues les yax^Ê^ trouves
l*hypotenufe.
Cherchez, premièrement les angles par ta ï.Prop^
&pHis après l'hypotenufepar laprecedente 6.Prop.
\
t> ■ I ■ Il
CHAPITRE II I.
i
1>e U fuffutation des Triangles rcdiligncs
obUqum^Us.
I. Pr G p. T^ Tans connus deux cotez > & un an-
X^gle opposé à 1 un d'iceux > trouver ^
. l'angle opposé à Tautrc : Moyennant quonf^acho
s'il eft aigu oh obtus.
Comme le coté opposé à tangle connue
Au Sinus du même angle ;
Ain fi {autre coté.
Au Sinus de (angle opposé a ce coté.
«. - ' ■ '
I L Pro p. Etans connus deux cotez > & l'angle
compris d'iceux> trouver les autres angles.
Comme lafimme des coteK, connus ,
A la ibfference des mêmes coteK 5 *
Ainfi
CHKt^lll.Des TrUfi^l. reEtil ohliq. x i
Akfi U Tangente de U m$iUé de U/hmme des angles
tncénnusy
A la Tangente de la moitié de lew^ différence*
Partant fi àla moitié des angles inconnus ( qui
(ont le complément de l'angle connu à i8o de-
grez^ la différence trouvée eft ajoutée , la fomme
icrale plus grand angle s & fi elle en eft ôtée > le
e (èra le moindre angle.
i
I. Pkq p. Etans connus les trois rôtez^troover
quelqu'un des angles.
prenez le plus grand côté pour la bafe > fiir la-
quelle combe de l'angle opposé une perpendicu-
lairei reduifant le Triangle en deux Triangles re-
ârangles. Alosfera
Comme la Bafi»
A lafimme des autres cotez :
Aifffi la JUfffrence des mêmes coteT^
A la différence desjdeaxfigmensde la bafe.
La difFerence trouvée étant ôtée de la baie , la
Mrpendiculaire divilê le refte en deux parties igtf
les. Ainfi donc aqx deux Triangles rcAangles
rhjrporenufè eft connue avec une jambe y par lèf-
queues on trouve les angles par la 1 1. Prop. du
Chap. 1 1.
EXEMPLE. Au
Triangle obliquan-
gle A B C > font
connus AC ii77>
AB8^5,&BC^M2
on demande quel-
qu'un des angles.
ë
J
Logariik
t'
t % Çk At ; I II; DesWtdngt. reBfL «1%
, Logarithmes. ...-,
Comtne AC 1177 -.--. ^.106x^0$
àABteC I4P7 3.i752z,8
AiniîAB-BC »3} — tii^Zi^? /
I AP 27J --r i,4j6j'868
N 0,T E Z.
On fétu M$ tramer le Logéirithme au ftMtrMt»
nombre re^MU , fi U cempUmm arithmétique tbt
fremier Logarithme r^uteli h refit Jtieeltef foutrait
4e icooçooopj efl fiouté àitx amres de^x^è-me
ieUfomm m '>te vers Uè^çheU fumier qÛaLè.
Çonme en i exemple precedetit. *
Logarithmes. '
AC 1 177: ^,8jj 8091 B
. Si m Lûgarithm ^pposi ne peut être /oâiraft d^
[tô. oooooop 1 comme, ceux êtes Tan^emês les arcs,
putre ^l deffrek s il lefaHtfiutraire de io.oào^6oOj,
^f4re comme devant. Ainfi le complément Arià-
ntetique du Logarithme de la Tangente ik è6 de^rity^
id^ 9^^Ai$^i%,^uiefi a^iftleï^gmthmedelkl
feme de fin complément.
^ Or A p ^7 î étant ôté de A C U77 > demeure
|>C 1 004, dpat la moitié 501 eft CE bu ED.
Maintcn^t au Triaiiglc rcàangle A B E çft çon-
^Chap.III. DestrUngireStilobliq. 15
nue rhypotenufc A B &S5,&lajiimbc AE 77 f>
par Icfqueiles on trouvera l'angle ABEr â.) d: 4g'
èc Tangle BAE 26. d: 21'. Dt même au Trian-
gle rcétangle C B £» cft VhyM^çjmfiP C^M f-ySc
h jambe CE 502, par lerquelles O0.trpavcrai'aar
gleGBE 52 d: 5 5». ac l'angle BGE 57 d; 2.5?. SB
v<Hi$ ajoutez Tangle CBE 52 d{ }.5^ài!angIcABË
é 3 d: 3 8Ma,fonune eft l'angle ABC 1 16 d: 1 3'.
A V T R E M EN T.
Ajoutez jenfèmble Içs troisxQtpz^Sc, ^ç, Ifi, mç^
tic de le^r foipipe fou^rayez chaque cgté comprer
nant l^an^le requis > pour ay qir l^ur.s " différence s.
Alors ièra
hCo^e qmlqMundèscotéTcotnfnrenans f angle rtf^tî^
Aqn^lqumedis^fferencfstr^M^lée^'i,
Ainji'fémtrediffirencey
A un quatrième nembre.
2. Comme Vautre cmcomprenévtt tan^c requU^^
Ah Sinus total ;
Ainfiie quatrième nombre trouve^
A unfiptiéme^
Ce feptiéme nombre étant multiplie par le Si-
nus touLla racine quarréc du prodi^it fera le Sinus
de la moitié de Tangie requis.
Ou plus facilement p^r Logackbimes.ajoûtes; le
..Logarithme du Sinus tot^l au feptiéme Logarith-
me > la moitié de la fomme (èra le Logarithirie dfi
Sinus de ta moiti é de l'angle requi s.
EXEMPLE. Au Triangle précèdent foie
requis Tangle ABC
^•^ c 4 Les
^
j
?4 Ch A v.lU. Des friangiremi obtiq,
TAC ii77
Iescôcez<^ A B ^^j
CBC 6%x '
La fbmme des côte« 1774
La moitié de fa fômtne 1387
La différence de A B , ii le Log.^.7 , ytf 70/
La différence de B C 7 n le I-ogi»S775>4.g4
T T L . lafommc;.55y6i74
Le Loganthme de A B 8<îy *.9 j 7c 1 ^7
Le Log du 4.avec le Log.du Sin.toul iII^JSô^
Le Loganthme de BC Ô32 1.8007 171
Le Lo^u T^vecle Log^du Sin.total T^JT^^UTx
La momeeft eLog.duSin.de j8d: éf9.//85,4lî
Le^d^ouble d-iceluy .77 d: , j'. eft l'angle req4^
^2^A^^^^ *^°^u" *f complemens Arithmcti-
ques des Logarithmes des cotez cqmprcnans l'an-
gle requis, aux Logarithmes des differen ces ttou-
vecs : la moitié de k fomme fera le LogariAîtoc
du Sxnus de la moine de l'angle requis-clmmc au
même exemple. t
Logarithmes.
Les cotez (^88^5 7-o6io8î5> compl.Arithro.
T jff /^^ ^3 i 7.1991829 compLArithra.
1-a difter. deAB/ii 4.717670^
La diffcr. de B C 7^^ i-Biy^^è^
Lafomme 19.857884^ !
l-a moitié de la fom, 9.9289411 comme devant.
JV.PKor.
G H A ip . 1 1 1. D^5 TrUngl: reBîL obliq. i j
iv. Prop. Etans connus les angles Se un côtéi
trouver quelqu'un des autres cotez.
Comme le Sinutde V angle opposé au coté connu»
Aucotécontmi
Ainfilç Simu de l'angle opposé an cSfére^tds,
Ah cotéreqms.
V. Prop. Etans connus deux cotez , &ranglc
compris d'iceux» trouver le troifiéme
côté.
Trouve'!^ premièrement les autres angles par^ lé
2. Prop. de ce Chapitre , &puis après le cotérequie
par la précédente 4. Prop^
CHAPITRE IV.
Vu cmIcuI des TrtMngUs Sfhericjues relf angles.
Obse rvations.
I. ǻI une des jambes eft Quadrant^ l'angle op-
i3posé à cette jambe ièra droit : fî moindjrç
que le Quadrant > aigu : &c fi plus grande , ojbtus :
& au contraire.
2. Si une des jambes eft quadrants l'hypote*
nufe Ccxz auffî quadrant : mais , fi Tune & l'autre
d'icelles font moindres ou plus grandes que le
quadrant , Thypotenufc ièra moindre que le qua-
drant : & fi une eft plus grande que le quadrant>âc
iautrc
i6 Ch a r .1 V. iyes Triangl. Spheriq: nSf.
l'autre moindre , 1 hypotenufè fera plus grande
que le quadrant ^ & au contraire.
3. Si un des angles touchans Thypotenufceft
di'oit> rhypotenufe lent quadrant : niais^fi chaoïn
d'iceux cft moindre ou plus grândtqu4mxlroit J'hy-
potenufe fera moindre que le quadrant : & fi l'un
,d'iceux eft plus grand qu'un droit» & l^autre moin-
dre^l hypotenulè fera plus grande que le quadrant;
&: au contraire.
4* De tout Triangle Spherique les trois angles
font plus grands que deux droits.
I.Prop. Etant connu un angle oblique s &une
jambe adjacente à iceluy» trouver l'autre
angle oblique.
Comme le Sinus totaly
uiu Sinus de l* angle obUcfue connu ;
jiu Sinus du complément de U jamte connue.
Au Sinus du complément de langle requis.
I I.Prop. Etant connue une jambe> & un angle
oblique opposé à iccUe » trouver l'autre angle
oblique i Moyennant (juonfçache s il efi aigu ou
, ^btus : ou bien fi l*hpounu/iy ou l*amre jaimkt > efi
,. moindre ou plus grande que le féadroftt.
. Comme le Sinus du eompfement de la Jambe connufi
jiu Sinus du complément de C angle conmi y
Ahfi le Sinus total,
jik Sinus de Sangle requis.
a .»
AVTRB
C H A p. IV. Des trian^. Sfèfriq. n0. xj
A V T R B M E N T.
ComtHe le Sinus mdl%
A U Sécante de IdjdMhe connue i
Ainfi le $inm du complément de f angle connu»
^H Skms de l-anj^ re^ie.
i I L Etant côhtiuè' Phypotenufe > & une jambeib
trouvtlrl'aiigrfe opposé à cette jambe.
Cànifh'é USïnàsdJèl'Éyfârenàfi»
jiti Sinus tolaf^
Ainfi le Sinus de làjdmhè eûnnuë^
Au Sinus de l*an£le requis •
A VTK B MHKT4
Comme le Sinus tot4l%
A la Seçame du complément de (hy^otenufi^
Ainfi le Sinus de la jambe connue»
jiUSînus dé VangU retjUie.
\ y. Pro p. Etâns connues les jambes » trouver
lequel on voudra 4cs angles obliques.
Comme le Sinus total»
Au Sinus de lajamtf adjacente à l'angle retjuù^
Ainfi la Tangente du complément de i* autre jamhe%
A la Tangente dà complfnient dt l'angle retjuis^
V- Ph o ?. Etant connue lliypotenufe & une jam-
bej trouver Tangle compris d'icelies.
Comme le Sinus total»
A la Tangente du complément de rhypotenufii
^infi la Tangente de la jambe connue,
^ ^H Sinus du compliment de f angle requis.
vi-Prop;
1 8 Ch A p . I V- Des Triangl. Sfheriq. reâf.
V I. Pro p. Etant connue l'hypotcnufc, & un an-
gle oblique j trouver Tautre angle
oblique.
' Comme le Sinus totaly
Ah Sinus du complément de l^hypotenufe ;
Ainfila Tangente de rangle oblique connu,
A la Tangente du complément de P angle requif.
VII. Prop. Etant connue Hiypotenufe* &un
angle oblique y trouver la jambe opposée
à cet angle.
Comme le Sinus total.
Au Sinus de (hypotenufe ^
Ainfi le Sinus de t angle oblique connu.
Au Sinus de la jambe requifi.
VHI.Prop. Etant conhuë rhypotcnufe, & une
jambe> trouver l'autre jambe.
Comme le Sinus du complément dt la jambe connue.
Au Sinus du complément de l'hypotenufi ,
Ainfi le Sinus total.
Au Sinus du complément de la jambe reepti/e.
AVTREMÏNT.
Comme le Sintês total, ^
A la Sécante de la jambe connue :
Ainfi le Sinus du complément de fhypotenufi.
Au Sinus dti complément de la jambe requifim
IX.
-i
Ch AP. IV. Des triangl. Sphrq.reff, ay
I X. Pao ?• Etans connus les angles , trouver la*
quelle on voudra des jambes.
Câmme le Sinus de Vangle oblique dd/acent m U
]ambe requifi.
Au Sinus du complément de l'autre an^le oilij;
AinÇ le Sinus totale ^
Au Sinus dn cûmpUment de U jambe requife^
\
AVTKEMEIIT.
Cemme le Sinus total»
A la Sécante du complément de f angle obliqua
adjacent à la jambe requi/e ;
Ainji le ^inus du compl. de Poutre angle oblique^
Au Sinstsdu complément de la jambe reqmfi»
X* Pao p. Étant connue* une jambe > & un an-*
gle oblique adjacent à icelle^ trouver
laiitre jambe.
V Comme le Sinus total.
Au Sinus de la \ambe connue,
Ainfila Tangente de l'angle oblique connu,
A la Tangente de la \atnbe requife*
X I* Etant connue une jambe » & un angle obli-
que opppsé à icelle> trouver Tautre jambe t
Meyennane quon/fache fi eUe, ou bien thypotenu*
fe, efi moindre ou plus grande que le quadrant : ou fi
ï autre angle oblique efi aigu ou obtus.
Comme le Sinus total,
A la Tangente du complément de l'angle oblique
connu y
Ainfi
31 Ch A. p . I V. D« triangl. Spheriq. obliq.
gairc y &o peut ctrc faîte par les Proppfitions pré-
cédentes > je n'en diray niot> pour montrer corn--
ment on refoudra les Triangles fans l'invention
de la perpendiculaire par le moyen de detix Pro«
f^ofitions feulement : Et au lieu de pluiieurs paro-
es qu'il faut pour les exprimer ^ je le feray plus
brièvement par lettres. Ceux qui défirent en avoir
les demonftrations , les trouveront en la 77>jftf»p-
metrie Britannicjue d Henry Bri^gs.
Pour ce faire félon les Analogies (uivantes ^
marquez le Triangle proposé par les lettres A »
B> C> ccft à fça voir l'angle duquel la perpendicu-
laire doit tomber par la lettre A > l'angle connu
adjacent à un côté connu par la lettre B» & le
troi/îéme angle par la lettre C : & où la perpendi-
culaire coupe la ba(è à angles droits , mettez la
lettre D.Les angles étans ainfî marquez^ les cotez
de chaque Triangle reâangle feront auffi mar-
quez.
Si les angles B & C > ( touchans la bafe B C )
font aigus > la perpendiculaire tombera dans ie
Triangle : ifi B eft obtus> elle tombera dehors ou-
tre Tangle obtus C. *
• NOTEZ.
Puis qull eft dit que la perpendiculait^e doit
tomber du bout d un côté connu ayant ah angle
cohnu à l'autre bout y & que cela en quelque cas
( comtne de la i .4.9;& 1 2. Prop.) peut- être fait en
deux manières r partant en la 4. & 11. Prop. nous
advertirons d ou la perpendiculaire neceffairemenc
en cette rencontre doit.tomber. Aux autres deux' il
n*y a point de différence. , . *
I. Paop.
r
*• . Cii îlV y. Des ffriM^lSphtr^^ jj
|.pAor«£caii$ connus deux angles ».& ie o6té
d entre iceux > trouver le cx^éme
an^
1
!• Comme le Simts tPtéû,
AmSimu dm cèmplemeat dé AB
^linjS U Témgeme de ABC
AUTangemeducemplememde BAI>
£cant trouvé B AD fem^nifi^ aoffi CAD*,
z. Cemme le Simis de B A D
Ah Simu de CAD
Ainfile Simtf dueompkmeik de A B C
Ah Sitmi dtt cofkpUment de A C D
» '
NOTEZ.
En la première fc féconde figQir « A C D eft fo
même que ACB:maîs en la troifîétw» ayant trou*
vé A G D 9 il fifut preiodre (on compittiene à 1 80
4€^z > pour avoir Tangle re^8 A C S»
Pour montrer la facilité de calculer pair ces ana*
lôgics, je donncray unexempletaveç laplus htié^
itiànierc d'opérer.
Soit du proLïnier Triangle obliquangle BAC*
î ' ' connu
34 CHAV^.^sJhSKk^S^kriji.ùl^if
connu l'angle BAC io4dcg. 6. l'angle ABC
3% àc^ o^& te côté A S 50 4iteg. 6. on demande
TangleACB. -
I» ZûgétritAi
AB 50 (1.6. Sîoxompl. 5«y)7i||t^
ABC 3 > d. 6, Tangente 999x909$
B'D s s à' y 5'.Taii.coin.i^.8jp|404
1 1 PaoP. Etans connus deux côtcz » & Tangler
^ oppose à l'un d'iceux > trouver l'angle
compris d^ccux.
LfgénnA»
SLeo.M^5)xt
Sin. o.oM5&fa^c.
Sio. 9.371^14
» CD
• « I • I •
'■ ':
.1. Çoffmili Si9ms^i^4i ^
^Ainfi U Tmgime de
A U TdngemidMtxùmfUnum ék
AB
ABC
BAD
^ï C^nimUTmgeméJk ' AC
-^■^'■y:'i-:^JsTéf(g9me-di ' AB'
^ {j^fihSiMê$dut09^imentiê BAS)
c/Â^ Simt4tê chmplemtm ié ' CAD
' Si la perpendiculaire tombe dans le ^xiangie J^
fcitome de B A D , C A D : fi dchors^Ia Jitf^çnce
d'icenx eft l'angjiexeQuis B AÇ«
ULPro?.
|I I. Prop* £cans connus deux angles » & le cô«
te opposé à Tua d'iceux , trouver le rroiûénit
angle : Moyermani qtèon fçache s il ^fi 4igw 09$
étus : pH bien qt$e Péfece fk cité ofposék Péimr$
mtglt àoimi fiif cêuméé .
^ b'cd
!•'• » f • •
C JD
X. C9mm€ U Sinus toid^
An Sinns du cpmplment de A B
^infi U Tangente de ABC
t/[ U Tnngeme dn ccmptemm de^ BAD
u Comme le Sinns dm cemplemm de ABC
c/f» Sinns du tQtnplemem de B C A
, tAk^USmsdo BAD
M^ShHsd^ CAD
Si la perpfendicttf âirc combe dans Iç Triangle;
Ufomme de BAD> CAD: fidehors^ la di&reoc^
dlceox eft l'angle requis B A C«
ty^ Pro p. Etans connus deux cÂtez » ficl'aiiglf
compris d'iceqc : crouyer quelqu'un des
autres angles.^
En ce cas la perpoidiculaire dok aeçeâaî^niàit
tomber du côté of ^sl à Taagk ttq^s*
Ta iXenmt
5^ CuAV.y.DesTriMgLSfheriq.oUiq.
C B
I. Cimwu le Smtês taiéU»
t/iu Simts dm cêmpUmimde ABC
%/iin/iU Tangemêde A B'
^UTdngemiâc BD
Eunt trouvé B D« ic inaaifcfle auffi{C D*
. u Comme USkuuM ' CD
^uSmmii BD
\/tinfi U Témgeme de ABC
t/i U Témgeme de A CD
N O T £ Z.
.En la prcmîcre & féconde figure»! 'angle A C D
^le même que ACfi : mais en k croi£éme>
ayan( trouyé A C D > il faut prendre fon com-
plément à 1 80 degrez » pour avoir l'angle re*
*quis A C B.
V.Prop. Etans connus deux cotes s & Tanglt
opposé àl'un d*iceux > trouver l'angle opposo
à Taucre : Aieyemmnt fuenffache s*d efi ai^H
OH chus*
^CemmeteSbms du cotéeppesésfém^lecemfu^
f/^n ^ms de Vmn^ cenmj
Cukf.y.DesTriàf^L Spberiq. otli^. 37
f^mfi le Sinms de fmttre cfU eemtm^
AuSinm de Pdrtgle fefme.
V I. PiLO p. Etans connus les trbis cotez > trouver
lequel on voudra des angles. , '
Ajoutez en(cmble les trois côcez % &ile1a moî«
dé de leurfomme foàtrayez chaque côté' comprc*
nant l'angle requis > pour avoir leurs di&sences^
Alors ièra. - ^
I. C&mme le Sbnis de quel^un des cotez, cofhfrtMHs
trnigk reifHie^
Ah Shms de Csme des différences treavées*
Ainfi le Sinms de fMtre différence^
A wi éjHéttrieme Sdms» -^
2* Xlemme le Sinus de téimre cese ^emprenMS PéUt»
gle req$(iéy ,
%/tu Sinus tetdy •.
%Ain/i le efUéttrieme Sisms trettve,
^ un fiftUfne %inusi ' ill.
Ce ièpriénie.Sinus^tant multiplie avec le Shius
t^cal» la racine; quarrée du produit fera Iç Sinus de
Ufmiîdcderangte requis. ,V' ^ • -
Ou plus facilement par Loe^tKmes » .«i jouter
le Logarithme du Sinus total au fe^tiéme Sinus
Logarithmique : Iamoiti.é 4^ lajbmnpbe (era le Lor
ganthmç du Sjnus de la moitié de J'angle requis^
Ou bien ajoutez les comptcmens Arif hjtntriqMcs
des Logaritlimcs des Sinus 4^5. f ôtez icompren^n s
l'angle requis^ aux L0gariçh9>es.des Sinii; desdif^
ferences crouvces:U moitié delà romçiçierale Lo«
i 3 ' gàrithme
garithme da Stni» et h
moitié de 1 Mgle Mmis;
pont voicjmi exempte.
Au Tmngte ÂCD font
connus les câtez à D
41 é:9.ACi6à*;6. se
ە>^4^ 4^0ftdem2rt^
deFas^teACD.
tes î A^ 41.8'
^ AC 30.0
CD 14.4
côceir
La (bmme des cotcar
Iz moicié
ladifFer*deAC
tadiflfcndcCD
!(rjt fostinié
I,a moitié cft de
ic double dft
-♦- —
0.3010)00
5:491308}
5.^09880}
5^.896 j 860
dé A C D
ioj.5^
V I L pu o p. Etans connus les troi^anglf s^ trou*
ver lequel on voudra des c^'tez.
%ti changeant Ui atïglcs éû îeufs côtîli^cmpcK
0te > AT pnen^tnt âti lieu dtr phè ^tAti^ itipé ic en
€&ti opposé iiceluy. fe Côtapktpidtti ifôâé^
Î>tt» y rôperatioti ieta totitrfc nrénïe' càttixnt ei^
* précédente. V '
vif I. Pua 1^. ÈTâftrf<i<3rAntfs'dbnrâiigfës , êévM
t6ti opposé à V\jti d'idcui , trbiiveif fe tête Op-
fùsék rkutril : McjHer^Àm iptànf^éÊtbi sUefi
iHoihire où plus gtàfii èfie li ^étàhr.
Ç^mme le Shf$is détàHlttâMosiâHtiïéé^tmt^ ^
Ainfi
!
e/f/isry? /« Simu de tamf9 ànglt cwmu%
Ad Sims éké cité rt^ nk.
\ X*Pftop. Etani connus d^ux cotez > & l'^i^le
compris d'kçux > trouver tic troifîéme
*--► Cote*
Au Sinus Jh complément de
" i^btfi U Tangente de
^ jé4hiTéàegeàifdÊ ...'./'^u..
AfiC
AB
« î< ■ • *
II
AB
AC
%* Cêmme te Sinus dt$ complément de^^ .
wM S$mis m complément de ,-,,
Aihfi lé Sinus dû coimUmént dé '
JIh Sinus du complément de
}t:f%OT. Etans c<Kiiius dwif^ingles y 8c le côté
o^osé à l'un d'ic^9 Cflouver lé coté. entre
les angle^ connue : Me^Ciénéim ^onfçachéfijte
cité requis 9 M bien le fcoté ^pose* À l'mêtfM
mile connut ^ eft membre ou fUts irunét<pfo^Û
/
î 4
%• Comme
4© CHhv.V.l>esrrûingLSfhmq,Mf.
u ^Çamme le Sims MsU
Au Sims du cpmpUmim Je
^injl U Tsftgeme di
AlmTAfigêmtdê
n/i U TMrtntt à*
. jimSimu Je
ABC
AB
BD
ACB
ABC
Bb
CD
f] $i la perpendiculaire tombe <Uos le t^jîaogle,
Ufotmedc BD, CD :Ci dcHçrs , Ja.diffçFence
d'iclnlx cft le côté réduis B t. " '
X |. Prop. Etans connus deux cotez , & VinzU
; oppose a 1 un 4'iceux , trouver le troilTcmc
ÇOt€i
k I >.
*^ - k
» • ♦
<*'.■, «•
t. Comme
Ch a p .V. Bfs 7H0iigl Spheti^. Mit[: 41
I. Ctmme le Sinm totmL
Ati Sinus du complément de * ' ABC
^/tinfila Tangente de A B
ftA l^ Tangente de^ , ^ B P
±. Comme le Sinus du complément de A B
Au Sinus du complément de AC
^infi le Sinus du complément de B D
t/fn Sinus du complément de CD'
Si la perpendiculaire cotpbe dod% le Triangle»
la femme de S D , CD : fi dehors > la diffeience
l'iceux>^ft le cçtcé re^^s B C» ^ ^
\ - '
X 1 1. Pro p. ^ Ecans connus deux angles , Sch
côte d:*entf c ïccux y ttouver lequel oo .
yondta' dès autres dâteaî.** -
N O T Ç 2^
En ce cas la perpendiculaire doit neceifaire-
nent tomber de l'angle connu a4j^Cca]c au coco
.1 »
>i« 1 1 >
-\
• C&mme le Sinus totale
%/4h Sinus dM'CompUmem de ' - AB
Ainji U Témgente de , . v : l ABC
^UT^egemedsêx^mhmentdf i BAD
A c ' Etant
Staiit ttonvée \k D , (c twmfeftc auŒ CAD.
i. Comme le Simu dn etfnplement de C-A D
«/^« Simis du ceikpUmetit d» B A D
tAinfi UTângeme de /" AB
AUr«iigmed« iiç
ABREGE*
«
!• ^1r[Taht connue la P%S?aii4cobli^'t/cff
Xjï*EcImri)^uci &U Soleil ai
plus proche Équinoxe>trouver ia declinai/bn.
Comme U Sim^s total.
Ah Sinêtf àt ia'iifldfkédàplkst^éthé Efutn^ixt;
-^ihfiléSinusieldjdksp:Mdéàiltfiih/, ■'
tA^ Sintu de U deeUndu/in re^/h.
M. Etant connue la plus grande obliquité et
l*£cliptique J &la declinaifbn du Sofeu > trou-
ver le lieu d'iccluy dans rEchpti^c,
Comme le Sitms de UflnsgrdiHde ebUfêki de VEctr
pti^. " V. .
e/9i» Simu de U decUnsifin du SeleU 5
t/tiffi le Shms totédy , -
. \ Jtu Sinus di l4^4mê du Sfil^êH^froAe
K Efmmxe. * *• v ^' • V •.
' • V * crcwée
L
Airegé Àe ^^ftkM Afirmomieiêêes. 4^
trouvée par Tycho-^Brahe aj d: 3 1'„ jo". fiir la-
quelle par confequent il ^c opérer pour tes decU'*
naifons exaâes.
III. Etant connuH la plus grande obliquité de
rEcliptique , & la diftance du Soleil au plus
proctie Equinoxe » trouver Ton .Afceniîoa
droite.
Comme U Sinus mdy
An Sinus du'cemplimm àeUftûsgi^anieoUujtAtf,
AinfiU Tangente deU iifiénc€ du Sûleil 4» fbis fr^
,che Btfinmxey^
A la Tunginte de tAfcenpon droite re^ui/e.
iV^fitatit conniM la plus grande obliquité de
TÉcliptiquç ^ Se la dcclinaifon du ^oleiU
trouver (on Afcendon droite.
CmnmeleSkustHétf,
. ^A\ UTatigentedelMfUctinMifinjdM S^Ml: * .
Ai'itla Tmigente 4u complément de Ufùnsffrânde
, oilifuit^.
Au Sinus dé VAJctnfim droite refuije.
V> Evant cohnuè'4a plus grande obliquité de rE-
. clipti<^» & la diftance du Soleil au plus pro*
che Equin^xe^rtrouver l'angle fjpe T^^iptique
fait avec le Méridien.
* » '^'
CmmJ^Simêsfotaly:^
Au Sinus du eoft^lotum ^ l^difiance du Soleil
4M plus proche Eipdnoxe^ ^ ,
Aiftjs U Tangente de Utplûsgratiiè mitjuhf^
ktd TTétigem drè cômpt. dé tdngkViMk.
VL
yi. Et^t connue là plus grande obliquité de
rEcliptiquc, & k 4ccfinai(bn^u Soleil , trou-
ver l'angle que TEcliptique fait avec le Mé-
ridien. ' ' r: . ^
Comme le Sinus du eomptement de la déclinai fin du
SpleiU
Au Sinus dm eompl. de la plus grande oUicpAté^
Ainfi le Sinus tetal^
Jim Sinus de Vmgltrefsdsk
VII. Etant connu? la declfnaîfon du Soleil, &
l'clevatiop du Pôle, troutèr Tahiplitude Orien-
tale ou Occidentale du Soleir.
■* ♦
Commente Sinus du compl ^ Htevéuipn du Vêle, ^
Au Sinus de la dècHnaï/ifrdn Soleil f *
Ainfile Simts totale ^ f ^ '
Au Sinus de V An^lUs^sfiep^.
V II I. Etant connue la diftancedu Soleilaii j>bs
proche Equînoxc&ia^pltjs grande AmplitU'»
dç, trouver Içs autres AppiitiMcs.
Çennfse le Sinus total ,
AkSsnHsdéUplmgi^afiiUJimplitudeW
AinfileSinus de fa difianteatèplus proche E^tdfiosce
Au Sinus de tamplhHdéVeijuife. -' ■ >
I X« Etant connue la declinaifon du Soleil »&
1 élévation du Pôle, trouver la dif&rehcc* -
Afcenfionclle. ' - -
"» -«
Comme le Sinus totaU '
AU Tanieme delà dectinai/in du ioteil: "
# Amfi
Abrégeât J^flians AjlfMomi^pies. 45
Aifffi U Tétntgente de NUvéUiou du Pôle»
• . Au SioHfde is différence Afienfiene&erefnifim
X- Etant connue là declinaifon du Soleil» ic Tcle^
vation du Pôle/trouver l'heure du leyer ^
ou coucher du ScJeiL
C9mme le SiftHs totdt, /
A U Témgeme de U declméufin 4m S0UU :
AwfiU Tangente de fUevéUiendu IW#,
Au Sinus dHcemfUmem de i^urcfinànaUmm.
L'Arc feminoâume réduit eu tems » donnent
l'heure du lever du SoleiLqui étant ô te de ii.hett^
X6s> réftera Theurt du coucher.
X L Etant connue l^Elieyation du Pôle > & lleai»
du lever ou coucher du Soieilj trouver fà déclic
naifon j & partant à quel jour il fe levé âr cau^
che à rheure donnée.
ilemme le Sinus teiul%
Au Sinus àe U Sftémce du Seleil du Midft
Ainfi lu Tangente du cempLde Pilevéuien du Fele^
AluTàngemedeUDecUnéUfinreqt^
Maintenant pour avoir le jour auquel le Solcû
fe levé & couche ^ l'heure donnée » faites cette
analogie.
Cemmele Sinus de Ufdusgransleetliquiié de /*£•
• eliptifuèi
Au Sinus de la declinui/in ebê Saleilî
Ainfi le Sinus total ; ^ {E^uinexem
Au Sinns de la difianee du Seleil au plus prêche
XIL
4^ Alsirtgé àe ^fikn$ Aprmmk^
XII* Ec^iu: CQoni^'cleyaapo chi Pole^ i» djCLcIk»
nâéjlbn du Sc^eil « & rheuce dii joitCi ivpUTer
la hauccur 4u S olçil.
Cette Méthode Tuppcfe la pçjrpenclicalaiire cp-
rée du Pôle de THprizoa fur lé cercle Horaire dii
Soleil.
I. Comme le SiftHi têtalf
. A U Tangemedm cêm^emem de VéUvéniote
duPûUi
. Aii^U Smus ^ cên^temm deié JifiMceJtê Sa^
AU T^npente Jk fremiér arç trouve*
Dépuis lîx heures du Macia jufipies à &l hevatM
dufoir > ôtez la premier arc trouva de la diftatw
ce éa Soleil An Poic» mais il lefitmc ajoâcor députl
les fix hernies dxiiairia(qiies ï ÙL heuresdiMmacinj
foar arrose le fecoadarc ttwxvL
I. Comme le Sinus du compU dn premier éirctroiÊve\
Ah Sinus du complemem d»/ic4ndércppMve%
Ainfile Sima de NUvaUon dse PiU»
Au Smus de U bmuur re^fmfe* ,
Pour trouver la h^Keiic 4u&)ieil à fix heureSi
fuiv«z ce^ce auaipgie.
Comme le Sinus totaU
Au Sinus de la declinèU/on du Soleil :^
Ainfile Sinus de Nlevation du Pote,
Au Sinus de lu tfomeur refêti/i.
Pour avoir la hauteur du Sofeil ati rems des
£quinojies> dites»
Comme le Sinus totul ; - ^
* Au Sinus dis 4:omfkmem de Viievatim dm P^le;
Ainfi
Ah Sinus
XIII* £«Mr<omm i'Atitt^ Se b declbaifon
és[%^éX >-a vec l'iicoïc dtr j6ar » trouvet
la hauteur du Soleil*
C9fmm h Sims dcfJ^mmb JtiSfleU du Mtfi^
An Simîs dn compliment içjfk deçtinmfun;
Aîitfi U Simts dcfk Sfiance du Ail^
Ah Sinus du complément de la namet^ reqmfi.
» -" « '
XIV. Etant connue la declinaifon j la haumitf
& l'Azimuch du Soleil» trpuyer \%cox^
du jour.
Comme le Sinus du cen^L de U declinnifin^
,^Sitms^fop»pkmm4ft(^iiamem%
^i^hSkm^^4^vmf^4^Mw^n^
Cette queftioa eft-fbrt uâlc pour rrouver Thcu-
rc plus facilement qjjc par la ISjirante , pourvu
i|8^ gfétmc ligne ^eriiîiepe Horizontale bien
i|ftc^e> ou un^on Aima»t : parcequè obfcrvant
•¥€«' iWbcr d\in fil^ l'^angte de TAzimmh ea
«aime tàns ^ la lutpteur» vous auroe rkeure par
Imelteate anabeie. - • •
V
naifoni & la hauteur du SolciU ttiwver
^Qj^t^z $it(m\:^^atif trois : Le ç^j^cmtmt
i,' . de
4:8 Ahregé de £^Jiim$ Afirûnomique$.
Àc rélevacion du Polë ; ladiftancedu Soleil dti ,
Pôle , & le complément de la hauteur du Soleil ^
& de la moitié de leur fomme foûrrayer le com-»
, plcment de Fék vacion <lu Pôle j & la diftance do
Soleil du Pôle 9 afin d avoir leurs différences*
Alors (èra»
I « C(mme le Sinus du compUm^m de félivmwn
du Ppte,
jiu Sinus àe Puni des d!fflsrenc€Str$9i^é€ti
^infile Sinuide Faturedifference»
A un eptmriime Sinus.
X. Comme le Sinus de laJUfiance du Seleil du Paie,
^ Au Sinus tosuly
Ainfi le ijuatrieme Sinus treuve»
A un/iptiéme Sôntir.
Ajoutes le Logarithme du Sinus total > auic*
ptiéme Sinus logarithmique : la moitié de la
tômme (èra le Logarithme du Sinus d'unarc > le-
quel étant doublé & reduit^enhmres j dqeoera la
diftancedû Midy.
Ou bien ajoutez eniènible Içs compl?l|iens
Arithmétiques des Logarithmes du Sinus ^i) çoti^
plement de Télevation > fie du Sinus delà d^ftaiHCC
du Soleil du Pôle > & les Logarithmes dc^ Sii^us
des diflèrences trouvées : la moitié de la fonaiinc
fera le Logarithme du Sinus d'un arc % dont le
«double jetant réduit en heures donnera la diftan:-
ce du-Midjr.
Cette queftioa tombe des plus en pratique, &
' fc rcfout-par la ^. Prop, du Chap V. des Obli*
quangles.
ydnglçs s Car au Triangle ABC , tc$ ttoig
.cpte« font ;don-
CçftlePokk .
B.l'Aftre.
AC> caœplcmciic de .
. la Latitude CK. **
A B > complcmcnc de
la bauceur B H.
B C ^ diftaace de TAftre au Pôle ^ qv ou rç^cen
6canc (a declinaifoa de 90* d^grcz ^ qutad eÙç kA
Septentrionale > & lajoûtant à po. degrez ^ lors
qu'elle eft Méridionale , & que la Latitude eft Se-
ptentrionale : car fi elle écoit Méridionale ^ il fau^
droit opérer tout au contraire.
LereéfftsfçA langk ACB« oui la diftapce dt
l'Aftrc B au Méridien lA meiitfée par Taircd^
l'Ë^aateur IL^ qu'il efaiic tieduire «il biures « en,
Icdivirancpafer i;.
Ot cette QaeftionTe reTout plus facilemei^e
px le dccoier précepte >x'cft à dite par les cooh
plemens Arithmétiques > que pas les auti;es çpc*
rations.
Etant connue V Elévation du Polct U hautenr , & lé
BeclinaïfinitHne Etoile , trouver £hewrii
deU nuit.
Il Êmt faire comme pour le Soleil'» & on aittÉ
l'angle A C B > ou ia diftance de rSnoile aU Mi<*
ridien y laquelle il faut ôter de fon AfceoiîoD d(oi4
te> fi l'oblèrvation eft faite dans la quarte d'O**
tient 1 ou lajoûter > fi elle eft dans la quarte
6 d'Occident*
5© Ahregé de ^fiions Aftfommquei.
d'Occident : te on aura l'Afcenfion droite dtt-
milieu du Ciel ^ de laquelle enfin fi on ôce VhC^
cenfion droite du Soleil ^ reftera la diilance du
Soleil au Midy pafsé » laquelle réduite en tems
donnera llielite lequife* Mais > notez que (i TAf»^
cenfion droite du Soleil fe trouve plus grande que-
celle du milieu du Ciel > il faut ajoutera celle--C]r
3<6o« degrez > pour en pouvoir fou traire celle-là»
ftfin d'avoir la diftaoce requile du Soleil du Midy
^afâéj qui eft Thc^eque Ton cherche^étant redui«.
te en tems à 1 5 .degrez pour heure.
È$émt ccntm le lieu du, Soleilytè' l* Elévation du Tolcy
tromper P heure du cemmencement &fin des
CrefufcHhs.
D'autant qu'on détermine ordinairement U
durée des Crept^cules par ^le cems qi» le Soleil
étt àbaifsé fous l'Horizon > jufques à 1 8. degrcz)
étant certain qu'il employé le même tems à dei-»
cendre de i8. degrez de hauteur jufques en l'Ho*
rizon que de l'Hodzon jufques à 1 84 degrez au
dedbus^ qui eft le Crepufi:uledu ibir^& de même
à monter le matin.
De façon qu'ayant l'heure de ladite hauteur» Se
fçachant celle du lever où coUcher par la Queftioii
I o. leur dif&tencc fera la longueur du Crepufcule^
laquelle étant otée de l'heure du lever du Soleil^
fôus aurez le commencement du jour > & étint
ajoutée à l'heuctdo coucher du Soleil ^ vous aurez
k fin du jour.
XV L
Jhfi^ de J^efiiom Afirmomt^s. 15 f
X V L Etant coatiuif r£levackm du Polc > la D<-
cliiuûfon ic la hauteur du Soleil > trouver
fon Azimudi.
Ajoutez enfemble ces trois : le complément de
rElevacion du Pôle > la diftance du Soleil du Pp-
le>Sc le complément de la hauteur du SoIeit>&; de
la moitié de leur fomme (butrayez le complément
de rElevation du Pôle > & le complément de la
hauteur du Soleil > afin d'avoir leurs différence.
Alors fêraj
I. Comme le Sbms ducemplemAttdetElevmkn
du fùltt
Ah Sums de Vune dtt différences trempées i
Ainfi le Sùtus de Vmàfe différence^
A un (jpsmriime Sinus^
a* Comme le Sinus du complément de U huuteur du
Soleil,
Au Sinus total,
^infile quatrième Sinus trouve^
nA un/eptiime Sinus.
Ajoutez le Logarithme du Sinus total, aufe-
ptiaoe Sinus Logaridunique : la moitié de la
fiHume icra le Logarithme du Sious de la moitié
de TAzimuth requis du Septentrion.
Ou bien ajoutez enicmble les complemens
Arithmétiques des Logarithmes du Sinus du com*
plement de l'Elévation du Pole>& du Sinus du cô-
plement de la hauteur du Soleil , Se les Logarith*
mes des Siaus des différences trouvées : la moi--
ô 1 tié
54 Mrigié ie ^m^w A^ifmmu^i,
tié de la fomitie fera le logarichmc du Sinus cte
la jnûicié de I Azimuch requis du. ^kptcutriôA.
Cctrc ^ucftion fç refouic qomm^ Ja pc cccdente
par la G. Prop. des Obliquants » les trois cpces;
du Triangle ABC étans doiuiç^ en la figure de
cy-dcvant:caf ayant trouvél'-ingk C AB/ôn com-
blement B A iaou H A M fera TAtiltiuth requis dM^
MidyàrAftrç. ; ' ;
ÈHe eft fort utâè pour la Gnomoniàiue & vàrU*
iton àè VAymant , car cti bbfcrvant la hauCeûr du
Soleil oh jpeut marquer fur un plan Horizontal
l'ombre d'un filet perpendiculaire ; pbis > l'angle
Ai^imuthal i^cant trouvé par le csilcàU âc trace liir
ledit plan > on a ou la ligne Meridiene , ou la ligne
Onmtede f félon qb'on a pris le complément dç
Tanglc C A B ^ 1 80 ©u 90 dcgrciè » ) par lune
ou l'autre defquelles on erouve la vatiation ite
l'Aimant.
Pour faire les Tables d'Azimutb f fervans a fct
Gnomonique & Quadrans de raiguillc aymaa*
tée y ) il uiffit d*y mettre les commencemens desi
Signes. D. Henrion en a fait pou^ plufîeurs £le*
vationp danç fan Traite des Triangles Sphcri*
ques." ^ \
Pour ticurèrl'Asimuth du Soleil à^. htwc^^
liuvwe cette Atudbgit.
C$mme le Sinuf tôt ait
Ah Sinus Ju compl de VÈietfâtion du Pcte^ ,
^infi la Tangente de la Declinai/in au Soleil y
jfi la Tangente de tjl^immh du SpUil vefi
ke %ptentri<fn\
pOHt
Four tfouvet rAzimuth du Soleil m. cemi des
Eqiiin&xes j faites cecce «nalogic*
Cûmme le Sinus tù$Àl%
A U Tétngentt de fEhvMien du ScleU ;
AinÇ U Téingeme Àe tElevmion dm Pôle,
Ah SktHs Jm cemphment de l*A^mtêfk re^ms
duMeridim*
X V I î. £)cux hauteurs de Soleil ou de quelque
Aftre ( dont la Declinaifon foit connue ) ctans
ob/èrvées en un jour ou en une nuit 3 avec leur
difFcrcnce Azimuthalc ; trouver TElevarion du
Pôle, âc Iciu: Azimuth.
AB CD cftic Méri-
dien.
C Zeàîth. Pôle.
fiEF l'Equateur.
AI L l'Horizon.
69 & H^ k Soleil j ou
l'Emile^
&£*& HK leur De*
clinaifon.
G/, & HF lemriuu^
ttur*
I F difïèrence Azinuitfaale.
Où dematide l'Ele^aticii éa Pde O Lé & l'arc
l'Homoti L F> ou A I^ OQ AF.
Puifqtfaa Triangle GCH , les deux cotez
GC, & H C rcomplemens de G I , & H F) &
j'ingle G G H r qui eft i'âirc If ; (i^tit connus ,
iWc G I*& l'ange G HCftretieauffi connus.
Mais
< •
♦ /
54 V jAreg/ âe ^efiim Jjlronomiqiês.
Mais , au Triangle G D H > les côret G D , &
H D, ( complcmcns de k Declinaifon G E, H K)
& GH étans connus , l'angle GHD fera auffi
connu 3 duquel fi on ôte G H C , rcftcra langlc
CHD : & partant dans k Triangle C HD , les
deux cotez C H , & D H , & l'angle qu'ils com-
prennent y étans connus , le côté C D fera auffi
ct)nnu> dont le complément D L eft i' Elévation dn
Polt. Comime auffi Tangle D C H^ qui eft lare
de l 'Horizon F L , dont le complément A F cft
1 angle de la ligne Mcridiene &: de TAzimuth de
r Aftre obfervé en H« Mais , fî on ne prcnoit que
F L y pour complément de 90. dcgrez , on auroft
l'Azimuth de la ligne Orientale Septentrional > /î
ledit arc F L étoit moindre qiie 90. degrez > ou
Méridional > s'il étoit plus grand.
Cette Queftion fèpeut aisément refoudreavdc
le compas iur un Globe > ou les Azimuths & Al-
mucantarats font tracez ^ en mettant la poinite
dLiGchvf ( ouvert des degrez H D ) fur les iK>ins
H3 G » &: fiaifant deux interférions de cercles au
point ï)j qui fera le Pôle 3 duquel on verra k hau-
teur D L, & l'arc FL.
L utilité eft grande pour k variation de tA^
mant > parce que en obfervant l'angle de quel-
qu'un defditsAzimutbs avec t'aiguille» on ^aît
celuy qu elle fait avec le Méridien > <»iand die eft
ar après trouvée » ce qu'on ne peutraice que par
es Amplitudes^ ou par k ligne Meridicne» que Ion
n'a point fur Mer.
£lle fert auffi pour k Gaontonicfue aux plans Ho-
rizontaux 9 mais infiniment plus en tous pkns
f quels
k
^
Ahigé âe Répons Afrcffomiquei. 5 5
^h qu'ils foitnt^ €h àh*
fcrvant deux poins d'om-
bre B 3 C> cie la pointe, d'un
%lo Oi » de Tincidence de '
kwiueUe Â# cirant ckux li-
gnes AB> AC> on aura
l'angle ou diflei:ence Azi* ^
mumale B A O la longueurt
de chaque ombre A B > A C> & la Hauteur du ftyle
AD, donnera la hautleur du' Soleil âir. ledit plan
lors de chaque ob(èrvatiO|^«
Partant on eft dans les
termes de la queftion» par
lefquelson trouvera lan*
gle de la Jigae Meridiene T,
diidit plan ( qu'on, appelle
ligne dm Style ) avec quel*
fu'un des A^imuths A B,
ou A C ^ laquelle ligne Meridiene ayant tracé fui-
vant ledit angle , & (ùr iccUe F A E élevé le fty le
perpendict^aire A D« on fera l'angle ^ P E com-
plément de la hauteur du Pôle fur ledit plan » la-
quelle on trouvera comme il a été enl^igné cy-
<fevant.Le point £ fera le véritable Pôle ou centre
du Cadra de ce pian^duquel abaiflant ou traçant la
Véritable ligne Meridiene» de tirant le i^ayon £qui*
noxial D F> on fera dans les termes de parachever
fedlcment le Quadrant , & de (çavoir { fi on veut)
rélevation du Pôle du lieu > la DrcUnajifôn du
plan^ &c* Mais, il fe faut fervir du jugement en la
détermination de la Declinaifon^ Inçlinaifon , Se
autres cixciviftamces $'4 y^^f^^ fi^va^t les Rè-
gles
€ 6 Akfegé àe ^flmt Afrmmipeh
glcs de ii Cnomoniquc qu'il fcroit trop long 4«
déduire icy paiï le menu.
X V U I. Etant connue l'élévation du Pote , & la
diftancc du Soleil au Méridien ( qui cil l'hcuïe>>
trouver l'arc de l'Horizon compris entre icekiy
Méridien & le ccrclettotatrc. '
Comme le Sinus totale
A$^Stmis de lElèvmion du Tole^
Ainfi U tangente dfi U diftame dm Sçleil 00
Méridien^
A la Tangente de Parc refHU,
Par là t>n few facilement & avec j^ftcflc un
Quadrant Horizoatal, parce que ces arcs de l'Ho-
mon font fcnfiblcment égaux aux angles des li-
gnes Horaires avec la Mcridienc.
X I X. Etant connue la Longitude & la Latitude
d'une Etoile fixe, trouver fa Declinaiton.
AEB cft l'E-
quateur.
P,fonPok;
le Zodià^e:
2,fbnPole.
APZ,Coli»:edes
Solftîces.
C^> l'Etoile don-
tiée>de laqucl-
IcG V^ fa Lon-
gitude > G C fa Latitàiiefoii» connues.
\
Mnregé de^uefiiàfh Aftrénimiqiêii. 5 7
U faut trouver C h> qui eft fa Dcclinaifon«
L'Arc PZ cft connu ij.d: 31. jo'. (^fçavoii: la
làiftance d un Pôle à l'autre ^ ) ZC cft auili connu»
étant le complément de G C* Et l'angle compris
P Z C eft auiu connu > comm« étant la diftancc de
l'Etoile au Colure connu^pUifque Tare VG>qui b
jueiiire » eft connu»
Parcant l'arc P C fera connu j dont le compU««
ment C £ eft la Declinaifon requifc*
X X. Etant connue la Longitude & la Latitudi^
d'une Etoile fixe > trouver fou Afctnfion
droite.
En la figure cy-dediis ^ Tare de l'Equateur VB#
cft l'Afccnfion droite requifc. Au Triangle CPZ,
les deux cotez P Z,C Z3& l'angle compris d'iccut
ctans donnez > on aura l'apgle Z P C » qui mefurp
hrc B E » le complément duquel pat deiTus <)ô.
. degrés eft le requis V E '• ledit ^rc B E pdurroic
^ éorc auffi HàOindre que 90« degrés > mais toujours
l'arc V^ E eft le complément à p o. degrés de l'an^
glc ZPC* Le jugement opère le refte.
Les ufagti àe$ DcçUnmfins des Etâites/im de ttoHi/âr*
y L'Elévation du Pôle par leur plus grahdc
iiwteux.
1. Les Amplitudes ortiveS» 6c pattant la viiria*
tionderAymant.
r j . On les place plus facilement fur les Aftt:olab6d«
\. Les fegmensde leurs Parallèles deHiis & de(«»
foiA THorizon.
J* Coiabicaelles padcnt prés ouloin du Zeniih.
6. CeUes quiibatcaujQUts^oune moateftcj^-
nais Tut i'HsfnzQu^ t
tt Les
-j 8 Ahte^ dt £^^fliM$ Aftronomiquef.
•Lis ufîiges des ji/lenfions droites fint de /Ravoir ^
1. Le tems qu'elles ptf cèdent ou fuivcnt le
$olcil.
2. Quind elles viennent au Méridien pour les
©bierver. - -.
3 . On les place plus aisément fur les Aftrolabes
-& Globes, -
Enfin, parla D^ecHnaifon, l'Afccnfion droite. Se
4a hauteur de quelque Etoile, on fçait l'heure delà
nuir,6on)me nous avotis dit cy^devant.
Il y a des Tables des Arccnfions,Declinairons,i
J^Si^diadons, Longitudes, de Latitudes dc« Etoiles
uiansles Sphetiqucs de D« Henrion , & chez tousi
tes Authcurs.
"5C5tI. Etans connues les^ Longitudes & Latitu*
des de deux Etoiles ou Villes, trouver leur di*
ftançe » ou larç du grand cercle compris entre
elles,
• •. -
B , C font Etoiles > ou
ViH^s,
îftylc Rôle. . ^ - . •
B D > & E C , Latitudes
Ubhhéés. . I
P. , différence des Lon- '
gitudes.
Donc au Triangle
ABC, les cotez A B,
A C , & l'angle cothpris
A, mcforc par FarciyÈ^ct^n^ cbmiùs ,B C le fera
«yili par la p.Prop.dc$ Obliqûangles*
»i^ /X^ ^^F
Ahregé âe ^éftms Afir^m^niques. 5 9
XXII. Etant connue la Declinaifon du Soleil^
TElcvation du Pôle :i & l Angic Azxmuchai^^
par lequel on a la lig" M«:iaicnnc , trouver
rheurc,
D B F,cft le Me- *
Tfdien.
Bile- Zenith.
C, le Pôle.
D F, l'Horizon.
H E > l'Equa-
teur. -^ JE
lA, Parallèle du Soleil A.
A M > la Declinaifon j laquelle étant, connue j
l'arc A C eft donné , qui eft Ton complément.
B C > diftan.ce des Pôles » qui eft donnée ^
aufli-bien que l'angle D B N A^imuthal par ob«*
fcrvation.
Donc au Triimglc ABC, deux cotez A Ca
C B , & l'angle C B A complément de l'angle
D B N > ctans donnés > on trouvera l'angle
B C A , qui eft l'arc I A ou H M ; lequel étant
Âiyisé par 1 5. dêgrez > le quotient fera le nombre
des heures requifcs.
XXIII. Etant connue la Hauteur & la Decli-
naifon du Soleil y avec l'angle Azimuthal,
trouver l'heure , & l'Elévation
du Pôle.
L'arc BA complément de la hauteur du Soleil
A N eft donné > A C eft auffi donné > l'angle Azi-
muthal eft auffi doiuié \ Donc
u X Cùm
^o Abrégé de ^Jiioris Ajlrùmmi^uei,
Comme le Sinus de tare A C>
£/? 4U Sinus de V angle ABÇ^
Ai^fi le Sinus de AB^
Eft au Sinus de Pangte A C By^ui ejl tare lAt
ou fi M 9 pour e heure retjuife.
Et pour'î'ElcvatiOnchi Polc, voyez TAnalo-
gie pour trouver le coxé B C> complcmcnt de k
hauteur du Pôle QV.
CANON
r
T A B LE S
. t
D
S I N U S.
TANGENTES.
SECANTES:
ET DE
LOGARITHMES
Pour lès S I N V S & Tangbntbs.
-«-
•**• .
I
9
I
1
2
4
5
lO
10 581.77 581.78
11
14
15
16
17
18
^9
Grad-
««•«i
Sinus
Z9.09
58.18
87.17
116.36
14544
^74-53
105.61
131.71
• 161.80
190^9
3iy^8
'34P»o6
57?.i5
407.14
43<^-33
465.41
4^4.51
^39'9S
6^^.04
6^8.13
717.11
75^.30
785.3^
814.48
843-^7
871.65
Tang.
19.09
58.18
«7-17
116.36
145-44
174*53
2d3{«6i
^0^9^ ^OOOOP^f
$19^^
34P-07
;f8.l6
4*>7-*y
43^-33
4^5^
4^4.51
yfiyécf
6^9*96
669^
6^8.14
7i7-»3
756.31
78541
Secans
100000.00
100000.00
100000.01 .
100000.04
I0OOOO/>7
iOOOOO,lK
100000.16
100000.11
100000.17
100000.34
jooo^.5f
100000.61
X090Ô0.71
100000.83
100000.^5
tOOOOI.Q|
I0O00I.11
looofj.37
TOOOOI.53
100001.70
xooooi/>f
100002.14
Z0000144
100001.65
XOOOOX.86
100002.08
814*50 100003.31
843.60 i 100003.55
871.69:100003.80
Log.Sin.
i^*.
6.4637161
^.76475«i
6.^408471
7.0657860
7.1616^60
7.141 877X
■ m
7.308813^
7.3668157
7417^681
7»46|7155
1^505 ii8l[
7.5419065
Log^Téut
^•7,^475^4
6.9408475
7.^^57863
7*1616964
7.141^78
7.308814S
7.3668x6^
7A^79696
7-4^37^73
7.5011105
7.54i^<^l
'7-57766B4
7.609S530
7.6398x60
' 7.^^78445
7.6941733
7*7189966,
7.7114775
7.7647537
7.78|:^4V
V.Î776715
7.6098566
7.6398101
7.8061458
7.8x54507
7-8439338
7.86x6613
7.8786953
7.8950854
7.9108793
7.9161190
7.9408419
7-667849»
7.6941786
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9834.46
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10010.71
10040.09
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00470.99
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100550.82
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100560.09
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9.019134^
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9.0204348
9.011 63 18
9.0228254
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9.0252027
9.0263865
9.0275669
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1869.18
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9.053 »88
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993S7'^^
17
i6
M
^3
II
20
18
17
16
13
12
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10
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9^2^4.62
862078.33
•59892.90
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9SSSU'6^
8T3401.72
851259.43
849127.72
8470Q6.51
^4^99S.73
84*795.31
840705.15
Secans
883367.15
881117.61
878879.57
972233^1
870040.^1
867858.89
865688/>5
863528.12
86< 379^)1
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832384.15
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9*9971993
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9.9^71559
9-9971AH
9-997^X6%
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9.9970976
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9.99^0535
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10.943340^
10.9422187
10.941099g
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10.9388703
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10.93665x8
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5^1^1.38
^891^6.84
J 881 13. 86
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Secarts
6o^88f.8o
60483 4r4f
603786.80
602742.82
*4 U8t9^.6o
>3
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19
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17
16
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10
9
98f5>4.74
5^8589.88
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98580.13
9857^*24
98^70.34
98fiM4
98^6o.T3
98^55.61
98ffOJ$8
5>8f4^-74
98^40.79^
601702.^0
6oo66ir.8i
J99632.74
^98603,26
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9«f3r-83
98^30,87
98f2T.90
98520.92
9851^.93
5>8T 10.93
595536.25
5945*0.98
593509."
59x500.95
5914^^-14
590494-7P
587080.42
586050.51
585024.10
584001.17
582981.72
581965.71
580953.15
579944«oo
578938.25
577^37^
576936.88
57594I'"' y 84558.20
5 98505.9*
4 98500.91
l 98495.89
589496.88
58S502.38
587511.28
586523.56
585539.20
574948.89,583580.53
573959.88 1582606.17
572974,161581635.10
* I
571991.73(580667.3*.
571012.56,579702.80
K
570036.63, 578741*53
* 98490.86 1 569063.94 577783.50
I
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9.994P^7
9^9919^1$
9^9919^1
9*9939391
9.9939178
9.993^1
9.993875 *
9.9938538
9.99383*4
9.9938109
9.9937894
9.9937679
9.9937463
9.9937*47
9.9937030
9.9936813
9-9936^96
9.9936378
9'9936i6o
9'993S9^^
9'993S7^3
9.9935504
9.9935*85
9'993^o6^
9.9934844
9.99346*4
9.9934403
9.9934181
9.9933959
9.9933737
9.9933 ^J
C 5
L0g,Tan.
10.7763935
10.7756181
[0.7748439
[0.7740711
[0.7732996
[0.7725294
10.7717605
10.7709929
10.7701265
[0.7694614
[0.^686976
[0.7679350
[0.767173*
[0.7664137
[0.7656549
ro.7648974
[0.7641411
[O.763386I
1 0.76263 22
[ 0.76 18797
ro.7611283
tO.7603782
[ 0.75 96292
[O.7588815
[O.758135O
■ ■ »
[O.7573897
[O.75 66457
[O.75 59028
[O.755161I
10.7544*06
[0.7536812
I
1
I
4
y
6
7
lo
II
II
M
ly
i6
17
i8
II
^4
lo Grad.
Sinus
7364.8*
735>3.46
742*1.11
74fo.7r
7^79-19
7508.03
7536-67
7565.31
755>3.P5
7621.58
7651-11
7679M
770847
7737.10
7765.73
77P4-3T
7811.^8
7851.60
7880.11
7^08.84
7P37.46
7^66107
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8023.30
8051. pi
8080.51
8109.13
8137.74
8166.35
8l^4.5>5
8x13 .55
17631.70
Tang. I Sccans
101541.67
01547.88
0x553.10
01558.33
7662.6P
76pi,6p
7711.6P
7751*65»
7781.70
7811.71
7841.71
7871.74
7P01.76
7931.78
7^61.81
7^^1.84
8011.87
8051.91
8081.95
8111.99
8143.03
81 73 .08
8103.13
8133.18
8163.14
8193-30
8313.36
830-43
8383.50
8413-57
8443-^5
8473.73
8503.81
8533-5»
01563.57
01568.81
01574.08
0157P.35
01584,63
01589.91
01595-11
01600.51
01605.81
01611.14
01616.47
01611.81
01617.16
01632.51
01637.89
01643.17
01648.66
01654/56
0165946
01664.87
01670.29
01675.71
or68i.i6
0x686.61
01692.07
01697.54
>i703j
02
Lùg.Sin. j Log* 1 ^9n
9.1396702
^.2403861
9.1411007
9*1418141
9'Z4zfi6^
9.143*374
9A^947t
9.1446558
9MSi6sz
9^^^6o69S
9.1467746
9.1474784
9.1481 811
9.1488817
9.145>5830
9.1501811
9.1509803
9ASl677^
9'^S^$7^9
9-1530675
9.1537609
9.15445 33^
9.1551444
9.1558344
9.1565133
9.1571110
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9.1585831
9.146^ 18S
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9.1477P3P
9.1485^^7
9.24^2643
9.149^^78
9.2507301
9.1514^1*
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9.152'92^00
9.1536477
P-i543743
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9<i558z40
9.1565473^
9.1571^^1
9'^S799oi
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9.1601 461
9.1608625
9.1615779
9.1622^21
9.1630053
9.1637173
9.15P1676
9AS99S09
9.26063^
9*1644283
9.1651382
9.1658470
9a66ss^7
9.1671613
9.167^669
9
5
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60
S9
58
57
16
54
53
51
50
4P
48
47
4^
45
44
43
41
41
40
Î9
38
37
3^
35
34
33
3*
31
30
79 Grad.
Sinus
Tang.
Secans
Lùg.Sin,
Lûg.Tan.
^8480.77
567118.18
575877.05
9>993$U1
10.7536811
P8475.71
P8470.65'
984^5 .y 8
56616^.09
565105.16
564148.38
574P18.61
573P83.33
573041-11
571101.13
571166.36
570133.60
9.P9331P1
9.9933068
9.993*845
10.7519431
10.7512061
10.7514703
^8460,^0
P8455.41
5^845 0.31
p844f,2i
98440.10
P8434.5>8
563294.74
561344.11
561396.80
9.9931611
9.9931396
9*993117^
10.7507357
10.7500011
10.74916^9
560451.47
55p511.11
558573 .01
56930J.93
568377-34
567453.80
9.^93194^
9^993^7^0
9.9931494
10.748538^
10.7478088
10.7470800
P84i5?.85
98414.71
9^19-16
557^37.86
556705.74
55577<^.63
566533.31
565615.84
564701.40
9.9931168
9.95^31041
9.9930814
10.7463525
10.7456157
10.7449003
98414.40
98409.14
98404.07
554850.52.
553P*7.40
553007.14
1éS7^9'91
5618B1.48
161971 ^99
9.99^0587
9.9930359
9.993013 I
ro.74417^
10.7434528
10.7417308
98398.89
P8393.70
98388.50
551090.05
551175.79
550164.46
561073.45
560173.86
55P177.IP
9.9919901
9,99x9673
9-99X94^
10.7410099
10.7411901
T0.7405715
98383.29
98378.08
98371.86
54P3 56.04.
548450.51
547547.88
558383.43
5574PI.58
556604.60
9.99x9114
9.99189S4
9.9918753
10.7398539^ ,
10.7391375
10.7384221
98367.63
98361.35^
P8357.14
546648.11
545751.11
544857.15
555719.50
554837.16
113917-^6
9.9918511
9.9918191
^.9918059
10.7377079
10.7369947
10.7361827
88351.89
98346.63
P8341.36
543965.91
543077.50
541191.88
553081.19
551107.54
551336.59
9.9917817
9.99x7591
9.9917361
10.7355717
10.7348618
Ï0.73 41530
98336^8
98330.79
198315.45^
541309.06
540419.01
53P55I.71
55046843
549603.05
54874043
9,9917119
9.99t6Z9S
9.99x6661
10.7334453
10.7327387
10.7310331
lo Grad
{
ta
P
30
5î
Sinus
8223.5^
825 2.1 f
928o.7f
850^.35:
154
.^^
3^
r
40
4t
4a
44
J6
47
48
49
50
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5f
57
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60
8538.08
î8f<^é.6^
Tang. Sccans
18533.^0
8563 .9p
8fP4.o8
8^24.18
8337.P5
8366.5:4
8j5'5.i3
«4*3 '73
84T2.32
8480.91
8W.M
8623.82
865^.40
■ »
8680.98
8709.5'6
8758.13
8766.70
8795.17
8823 .84
8852.41
8880.98
8909.54
8938.11
8966.67
8995^13
9023.79
9051.34
9080.90
8654.t8
8684.3I8
8714.49
8744.60
8774.71
8804.83
8834.95
8865^.07
8895.20
8925.33
89554^
8985.59
9015.73
9045.87
9076.02
9106.T7
91^6.32
9166.48
919^.64
9226.80
101703.02
01708.51
01714.0^
01719.52
9287.13
9317.30
9347.48
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9407.84
9438.03
01725.04
01730.56
017^6.09
01741.63
01747.18
Qi75i*74
01758.31
01763.89
01769.48
01775.08
01780.69
61786.31
01791.94
01797.58
01803.22
01808.87
01814.53
01820.20
01825.88
01831.57
01837.27
01842.98
01848.70
01854.43
01860.17
01865.91
01871.68
9.2606330
9.2613141
9.2619941
9.26*6729
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9.2640274
9.2647030
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9.1660509
9.1667232
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9.2673945
9.2680647
9.1687338
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9.1700689
9.2707348
9.1713997
9.17 10 5^3 5
9.2727263
9.2733880
9.2740487
9.2747083
»■■■ ^ — ^1>—ifc
9*^7$l669
9,2760245
■9.1766 811
19.17733^^
! 9.1779911
j 9.Z7%6^^
9.2792970
9.2799484
9,1805988
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9.267^66^
9.2686714
P.269374^
9.1700772.
9-^7077^6
9.2714788
9.2711780
9.27287<$2.
9.1755753
9.17416^4
9.1749644
9.1756584
9.1763514
9.1770434
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9.278424^
9.2791131
9Jr798oo^*
9.2804878
9,2811736
9.2818585
9.1825425
9.2.832251
p.2839070
9.2845878
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9.2859466
9.2866245
* >
9.2873014
9.2879773
9.2886513
79 Grad.
i6
^8304.12
13 ^8188.17
p8i8i.8i
98177.44
22
I
21
I
120
13
II
10
"8
7
6
7
4
3
98171.06
9^x66.67
98161.17
98iyy.87
981^0.46
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9813 9.6X
98134.17
98118.71
98113 .17
98117.81
98111.34
98106.86
98101.37
98195^.87
98190.36
98184.81
98179.33
98173.80
98168.16
98161.71
Tang.
38677.18
37805.38
36936.30
36069.93
3J106.16
3434T.17
33^6.^6
31631.31
31778.30
30917.^3
30080.18
X9^}S.QS
18391.f1
2^7552.51
16715.17
15880.35
15048.09
14118.36
13391-16
z%S66,^7
11744.18
10914.59
10107.38
I929X.64
18480.35
17670.51
16863. II
16058.13
If 115.^7
1445540
Secans
^— / .
54874043
47880.55
47013.41
46169*01
4^317.31
44468.31
41778.3 f
41^37.37
41099.03
40163.33
39430.16
3^f 99*79
37771.^1
36946.64
36113.93
3no3-75>
34486.10
33671.14
31858.61
31048.60
31141.09
30436AS
ii>633.54
1883347
18035.87
17140.70
16447*98^
15657.6B
14869,7^
14084.31
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9*99^661
_ (
9.99z6i^7
9*9926191
9*99i$9S7
9*992^S7^2
9^9911^^6
9*99iS2So
9>992Soi^
9.99*4776
9.99i4f3^
9.99*4301
9.9914063
9.99*3814
9.9913585
9:9^13346
9.99*3106
9'99zzU6
9>99^6z6
9*99i'i39S
9.99*1144
9.99*1901
9.99*Ij66o
9.^9*1418
9.99*1 I7f
9.99*093*
9*99^^6^9
9.^910445
9.9910101
9*9919956
9.99197^1
9*9919466
0.73*0331 i
0.7313*86 1
0.73061515
0.7*99*18'.
0.7191114
o*7i852i*
0.7178120
0.7171238
0.7164167
0-7257306
0.7250356
0.7243416
0.7236486^
o«7*i9566
0.7111657
0.7215758
o«72o886y '
0.72D1991
0.7195 II*
\
0.71 88*64 (
0.7181411 1
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o.7i^774^t
0.7160930 j
0.7154* »^[
0.71475*?!
0.7140^34^;
o.7l337fr
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0.7126986
0.7120227
o.7"3477
s*
II
Grad.
s I Sinus
1.1
o; 190^0,90
i
I
2
4
s
6
7
9
10
II
ir
^4
«7
18
Î9
21
141
iî
27
li
19
30
9138.00
9l66.SS\
925:2.20
9280.74
9309.28
9337.B2
9366.^6
9394-PO
94*3-44
5?4ÎI«5>7
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9jro9.03
X5>537.y^
K9f 6^.09
T9f 94-^1
19^313.14
I9^U*66
1^680.18
l:9708.70
19737."
197^^.73
Tang.
19438.03
j 946 8.22
19498.41
I9f 28.61
19158.81
19^89.01
19619^2
19649.43
^9$79M
19709.86
19740*08
19770.30
19800.13
^■^^^aai ■ *■■■■
19830.76
19861.00
19891.24
19921.48
I99fl.72
19981.97
20012.22
2.0042.48
2do72.74
20Z03.00
20133.27
20163.14
19794.21 20193 «Si
19822.76' 20224.09
19811.27120214.37
19879.78
19908.29
20284.61
20314.94
1993^-79 1*0341 •2-3
Sccans
1 01 871. 68
X 01 877 .44
101883.21
101888.99
101894.78
101900.18
101906.39
101912.21
101918.04
101923.88
101929.73
XOI93I.I9
101941.46
Il u t
101947.34
ioi9jr3.23
loi 919.1 2
101961.02
101970.^3
101976.81
10x982.78
101988.72
101994.^7
102000.63
io2oo6.6o
102012*18
I020I8.17
I02024.5f7
102030.18
102036.60
102042.63
102048.67
LogSin»
t I II
9.2801988
9.2812483
9.2818967
9.2821441
9.283190^
LogSTan
9.288^^25
9-%^99993
9.2906713
'■■■■■ ■ • ^— .^™^^
9*2913 42^4
9.2838319 1 9.2^2012^
9.2844803
9.z^Si^37
9.2817661
9.2864076
9.2870480
9.2876871
9.2883260
9.2889636
9.2896001
9.2902317
9.2908704
9.29X1040
9.292X367
9.29*7^8^
9-i93S99i
9.2940291
9.i9^^îo
9A9W^$9
9*1919119
9^9éS390
9*2971641
9>*P77883
9.29841x6
9A990^^9
9*i996SSS
9.2^26817
9.293 3 foc
9.2940x72
9.2^46836
9.2^jr3485i
9.*^6of34
9*1966769
9-197^39%
9*2p8ooir
9*19^661^
9.29932x6
9*1999^^
9.3006383
9.30x2^5:4
9.30x9^14
9.302606e
9.3<^26o^
9.3039143
9^0^1667
9.30^21 8j
9.3bT8é8^
^.306^187
9.3071674
9.30781^^
9.30846»^
If-
60
S9
58
J7
Ji
15
u
Si
To
f
47
4^
4^
44
43
41
41
40
39
38
37
3Î
34
33
3»
31
30
78 Grad
Sinus
98162.71
ySify.ié
^ifi.6o
^146.03
98140.47
98134.86
98129.26
^123.66
98118.07
98111.43
98106.80
98101.16
9809J.51
98089.86
98084.20
98078.5-3
98071.87'
98067.16
98061.46
9^^.76
98o5'o/>f
98044.33
9^38.60
98031.86
98017.11
98011.36
98017.60
98009.83
98004.07
97998.16
9799^.^
Tang.
Sécans
7144TJ40
714084.31
713677.63
711861.24
711069.11
713301.11
711710.70
711741.16
711178.77
710490.24
709704.26
710966.18
710191.74
7194ii.1T
708910.61
708139.18
1:07360.17
718671.18
717887.63
7I7I1I.18
To^î83.7i
707809.07
T07036.90
7I6379.M
JI5Î99.48
714841.9^
704167.00
703499.37
701733.97
714086.77
7i5333''8i
711783.09
701970.78
701109.84
700471. II
7 II 834.61
fi 1088.3 7
710344.31
499694.T9
498940.17
498188.13
709601.48
708^^1.84
708117.39
49743 8.Ï7
496690.37
497944-74
707390.11
706677.01
707916.06
497loi.if
4^H^P.90
4937*0.68
707197^
704470.66
703746.07
491983.78
491148.79
49x717.70
703013.67
701303.37
70x787.17
9.99194^6
9^9^19220
9-99^^97^
9*991^717
9.9918480
9.9918233
9.9917986
9-9917737
9-9917^9
9.9917140
9>99i699i
9.9916741
9^99l6^9^
9.9916141
9'99^990
9.99IT7Î9
9.9917488
9.99iS^S6
9.99^49^^
10.7113477
0.7066700
0.7079818'
ro.7073164
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9.991473 I
9.^914478
9.99I4»»T
9*99^^97^
9.9913717
9.99134^1
9.99IJ»07
9.991*9^1 I
9.99it69é
9.991*440
9.991*184
9.99119*7
0.7106737
0.7100007
0.7093187
0.7086776
0.7079874
0.7073183
0.70467 II
0.7039866
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0.6947817
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0.6934813
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10136,19
10164.78
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202^0.24
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20307.21
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20421.13
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2062042
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20677*34
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20734'2'^
20762.71
207^1.17
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2034^.23
20375.51
20405 .82
20436.12
20466.43
20496.74
20527/>5
10557.37
10587,69
2061 8.01
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20709.00
20739.34
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20800.03
20830.38
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20951.81
20982.18
21012.55
21042.93
21073.31
21103^9
21134.07
21164.46
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21225.25
21255.65
102048.67
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102054.71
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102152.69
102158.89
102165.10
102171.32
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102183.79
102190.04
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102208.85
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9.3123266
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21^30.35
21^8.7^
21^87.16
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21251 ^.6^
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21346.88
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10XXJ4.07
^01x40.40
0x146.73
oxxf3.07
X1377.30
XI407.7X
X1438.14
XI 468.^7
xi499*CO
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9.3184728
9.31906^9
9.320249f
9*3208400
9.3214297
9.3220186
9.3226066
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9.3x61174
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9.33609x7
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9.3385^7
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9-3403441
9.3409484
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9.34x1146
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9.3441180
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U
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M
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22169*47
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02447.81
22383-19
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02582.37
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9.3604736
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9.36163 19
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9
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1%
17
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11
21
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17
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II
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10
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4fi070.8j
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460111.16
4^^610.70
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135^16.17
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13608.19
13 639*00
Secans
01630.39
02637.19
02644.10
oi6fi.ii
%^ \ 13103.09
13131.38
%6
»7
18
*9
3P
13187.96
i33i6:*ijr
*3344-^4
1^669.71
13700.44
23731.16
13761.89
13791.61
13813.36
138^4.10
13884.81:
1391^.60
1394^-3?
13977."
14007^87
oi6f8.of
01664.99
01671.94
01878.90
0168T.87
01691.84
01699.82
01706.8 1
02713.81
oi7io*S2
01727.84
02734.87
01741.91
01748.96
01756.01
027^3.09
01770.17
oj»777.i6
01784.36
0x791^7
01798.59
©2805.71
01811.86
01810.01
01817.17
02834.34
0:^841.51
Lùg*Sin,
9.3Î10880
9>3Sx6^49
9.3 531 810
i>.3537i64
9.^54*710
9.3548150
9W3^*
9'S^S90O7
9»%S6^^6
9>SS 69^36
9.3^7514^
9.3^80637
9.3586027
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9.3591.409
9.3^96785
9.3601154
9.3^07515
9.3611870
9.361 8117
9.3613558
9.3,618891
9.3634219.
9'^^!i9S39
9.3^44851
9.3650Ï58
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9.3660750
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9.3671311
9.3676587
9.3681853
9.36«64i
^•363^401
9.3645 ly^
9.3650^01
9^3656641
9.5661374
9.3668100
9.3673819
9^^79S3^
9.3685-138
9.3690937
9-36966x9^
9.3701315
^ ■ ^ — ■
9.3707994
P.3 7 13^^67
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9.3714^^»
9.373o^4f
9.3736x91
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9.374^^^30
i?.3 7475:63
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9.3758810
9.37644x3
9.3770030
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9.3781x15:
9.3786813
9.3791 3 P4
9.3797969
9.38035:37
l
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f9
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$S
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49
48
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4^
4Î
44
43
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41
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38
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3<5
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34
33
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_ _i_j_L
97437.01
^7430.4^
5>743^3 ,5K)
97417.34
97^0.77
^7404.19
97397^^
97391 'OO
97384.3?
97377.78
Tang.
433147.^9
43 2-^73 -47
43200o.75>
43i4ï9.ry
9737X.i^
97364.^3
973^7.89
973 5^1 -M
97344.5^8
97337.5?*
43085:9.74
4302^1.36
41^7x4.40
4*91^8.8^
4283:94.71
42803 I.9P
4^7470.66
426910.71
42635:2.18
97331-*^
973*4.^7
97317-88
97311.18
97304.48
97^97-77
97i9i.of
97284.32
97x77.58
42^795.01
42^239.231
424684.82
Secans
444141^1^
443981.76
4434*3-8*
442867.31
442312.24
441758.5:9
441206.37
97270.84
97*^4.09
97*57.33
»»iaBiai«0iiimaBi«
97*fo.y6
97*43-78
97^36.99
424131.77
423580.09
423029.77
422480.80
421933.18
411386.90
410841.96
420298.35
4i97f6x>6
41921^.10
418675.46
4I8I37.I3
4I76OO.II
417064.40
[4165*9.98
440655.56
440106.16
439558.17
43901 1.^8
438466.38
4379**.57
437380.1^
43^839.10
43 6i9jpw^3
435761.13
435:114.19
434688.61
434154.38
433621.50
433089.96
— ■Il ■ ■ ^— — — — ^
43*559.77
431030.90
431503.36 I
430977.15
4304J2.2f
4299*8.67
429406.40
428885.43
4*8365.76
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9.99^7^39
9.9^^6947
9.9^^66$$
9.9886363
9.9886070
9.988577^
9.9885482
9.988J188
9.9884894
9.9884599
9.9884303
9.9884008
9.9883712!
9.9883415 i
9.9883x18
9.9882821
9.9882513-
9.9882225
9.98819*7
9.9881628
9.9881329^
9.9881029
9.9880729
9.9880429
9.9880128
9.9879827
9.98795*5
9.9879**3
9.98789*1
9.9878618
9.9878315
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0,63663^9
to.63 60599
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0.634 9099
to.6343359
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[ 0.63 20468
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0.6246810
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37
38
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^4007 .87
24038,64
2406^^.1
24100.1^
24130.97
24161.76
Sitius
^33^4-^4
2^372.82
23401,10
2342>.38
234^7.66
23485.94
i3ÎM-ii
23^41.48
^3^70.75
2'3fPP.02
23627.29
23683.81
23712.07
23740.33
237^8.59
2379^.84
2382^.10
i38î3-3T
23881.^9 i4y5>3.2o
24223.34
2:1-2^4.14
2^284.94
a43i^.7f
24346.^6
2r4?77.37
24408.19
3^4439.01
24469.84
Secans
102841. 52
02848.71
0285'f,9i
02863.12
24500,67
24^31-5^1
24562.35
23909.84
23.938.08
23966,33
^399^.$ 7
24021.80
24051.04
24079.27
24107.51
24135.74
24624.05
24654^
^^4685 .77
24716.63
24747.^01 '
^4778.37
24809,25
24840.13
24871.02
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:;!4i 92.19: 24^32.80
02870.34
02877.57
02884.81
02892.06
02899.32
02906.58
02913 .85
02921.13
02928.42
02935'-7i
02943-03
02950.31^
02957.68
02965.02
02972.37
02979.73
02987.10
02994.48
03001.87
03009.27
03016,68
03024.10
03031,53
03038.97
03046.42
03052.88
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5>-38o^7j7
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9.3^«i853
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9.3718523
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8.3749696
9.37Î4868
9.37^0034
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9.3780633
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9'379oS9^
9.3796015
9.38ori29
9.3806237
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9.3811339
9.381-6^34
9.3821523
9.3826605
9.3831682
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9.J836816
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9.3880837
9.388^311
9.38917^1
9.3897144
9.3902700
9.3^081^1
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29
28
27
116
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19
18
17
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97230.19
97223.39
97216.58
97209.76
97202.93
97t9è'09
97189.25
97182.40
97175.54
97168.67
97161.79
971^4.5^1
97148.02
97141.12
97134-11
97127.19
97120.36
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97ÏO6.49
97099'U
97092.5:8
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97085.61
97078.63
97071.65
97064.66
9705^7 ^^
97050.65
1 97043.63
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416529.98 4*?3^f -7^
415996.85
41 5 465.01
414934.4^
414405.19
413877.19
4133 50:46
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412824.99
412300.79
411777 .84
41 1256.14
410735.69
410216.49
409698.52
409181.78
408666.27
4081^1.99
407638.92
407117.07
406616.43
406107.00
4oy5'98.77
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405091.74
404585.90
404081.25
403577.79
403075.50
402574.40
402074.46
401575.70
401078.0^
427847.38
427330.29
426814.49
426299.96
425786.71
425274.74
424764.01
42425'4.5'7
42374^.37
423239.43
41*733-73
422229.28
421726.06
4212C4.08
420723.33
420223.80
419725 .45^
419228.40
r I
418732.52
418237.85
417744.38
417252.10
'416761.02
j'416271.14
'415782.43
415194-91
1414808.56
414323.39
;4i3835?.3^
'4^33|^-yy
1.
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9.98783 ij
10.6196463
9.9878012
9.9877708
9.98774^54
10.6190900
10.6185345
10.617979s
9-9977099
9*9^7679^
9.9876488
10.6174252
10.6168715
10.6163184
9.9876183
9.9875876
9.9875570
10.6157660
10,6152141
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9.5^875263
5'.9874^5
9.9874648
10.6141124
10.6135624
10.6130131
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9.9874031
9.9873722
10.6124644
10.6119163
10.6113688
9.9873413
9.9873103
9.9872793
10.610821^
10.6102756
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9.9872482
9.9872 171
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10.6091849
10.6086405
10.6080966
9.9871545»
91.9871236
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10.6075534
10.6070107
10.6064687
9.987061 I
9.9870298
9.9869984
ro. 6059273
10.605386^
10.6048462
9.9869670
9.986935^6
9.9869041
10.6043065
10.6037674
. 10.6052289
8
I
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2
4
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7
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14
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17
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24
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Z419Z.I9
24220<4I
24248.63
24276^^
2430^07
24333.2^
24361.^0
2438^.71
24417.^2
2444$.i3
»4474-33
245:02.1,4
24jr3o.74
245^8.94
14^87.13
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24643.52
24671.71
Zi699»90
24728.OP
2475:6.27
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24812.63
24840.81
24868.^^
24932.86
2-4^^3 «70
24^4.60
25025.5:1
25056.42
XÎ087.34
25118.26
zs 149.1 9
2^80.12
25211.06
25242.00
25272.94
41303 -8^
M334-84
25365.80
24897.16
M^l^33
24981.67
25009.84
»f 03 8.00
»T4»7.73
1^4^8.70
25489.68
25T40.66
Z^SSl'éS
25582.64
25613.63
25644.63
*r67f.63
Ȕ7o6.64
1^737.66
1^768.68
1^799.70
25830.73
25861.76
Secans
103061.35
03068.83
03076.32
03083 .82
03091.33
03098.85
03106.38
03113.92
63 i;.i. 47
03129,03
03144.18
03151.77
031^9.36
03166.97
o3i74«Î.P
031S2.22
03189.85
03197. S o
03205.16
03212.82
03220.50
03228.18
03235.88
03243.59
03251.30
03259.03
03266.76
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03474-5^1
03282.27
03290.03
9.3836751
9.384181^
9.3846873
5^-385^1914
9^1^^6969
9.3862008
9.3867040
9.3872067
9.3877087
9.3882101
9.3887109
9.3892111
9.3897106
9.3902096
9.3907079
9.3911057
9.3917028
9.3911993
9-39i'69Sz
9.393190!;
9.393^852
5^.39417^4
9.394<5719
9.39^1658
9.3956581
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9.3967711
9.3573089
5^.3^7,8463
5>.3p838|o
9.39^91^1
9'3994S47
9.3999^96
9.4005240
9^010578
9.4015910
9*4021237
9.40265^8
9^031871
9.403718%
9.404148^
9.4047784
9-4053076
9.40^8363
9.4063644
9.3961499
9.35^6410
9.3971315
9.3976215
9.3981109
9.3985996
9.4068915
9.4074189
9.4079453
9.4084712
9.4089965
9.4095111
9.4100454
9.4105690
9.4IIO92I
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4OIO78.OP
970Z9-S7
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9701 fufS
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969^7,10
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96973.01
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969s 1 .67
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9é9ùS.7S
96901, S7
96^94*39
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96871.77
96^USS
96818.32
3Î 968fi.o8
34 96843.83
53 ^^836.57
f^^ ~ 1 ■ ■ ■
31,96819*31
31196811.04
30196814.76
Secans
4i3356>yy
411874.87
411436.75
4IOP5P.67
410483.74
410008.^3
40^535.>6
409061.71
400581.65
400086.36 I412.3p4.35
399S9^.%3 411^14.^8
399099M
398607.39
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397617.1 1
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3^6165.18
3^680.11
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403478.7*
390417.10 403010.48
389^45.16 401563.31
389474.19 401107.11
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388535.74 40ii98a'3
388068.05 1400745.311
387601 U^ 400193.47
387135.84 35>P84*-67
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9*9Ui693
9*9^61369
9.9861045
9.9860710
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10.6031189
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16639.09
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14 Grad.
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03297.81
0330$. s 9
03313-3^
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03321.19
03329.01
03336.83
03344.67
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03360.37
03368.23
03376.11
03383.99
03391.88
03399.79
03407.70
03415.63
03423.56
03431.51
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103447.43
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03463.38
03471.38
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03487.40
03495.42
03503.46
03511.50
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9.3 5^90878
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9.4000615
9.4005489
9.41165 81
9.413 17?9
9-^13^993
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9.4147383
9.4010348^^.4^5 25 7C>
9.4015201 [9.415775*
9.4020048 J 9.4161^28
9.4024889 J9.'4i^8o99
9.40297341^-4173165
9.4034554^-41784*5
^•4035>378 ^.-4183580
9.4044196 9.4188719
9.415^3874
9.4195^013
9*4104146
9.4049009
9.4053816
9.4058617
9.4063413
9.4068203
9.4072987
9.4077766
9.4082539
9.4087306
9.4091068
9.4096814
9.410^575
9,4106310
9.4111059
9'4"57P3.
9.4120511
9.411524^
9.41199^2
9.420^*75
9^1143^8
9.42IP515
9.4114618
9.4219735
9.4134838
^•4239935
9.4145016
9*4*50113
,
9.4*551^4
9.4160171
9.426534*
9.4170408
9.42754^3?
9.4180515
6
75 Grad.
Sinus
20
i8
17
I5
If
H
13
i&
II
10
9
1
7
7
4
2
I
301^6814.76
1^1^6807.47
18 ^6800.18
17 ^67^1.88
161^678^.17
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96716.77
96719.38
96711.99
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96697*1%
96629*76
96682.33
96674.90
96667*46
96660.01
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9664f.o'8
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96630.12
966zi,6^
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386671.31
386207.82
3«f74^37
385283.96
3848x3.58
384364.24
383448.61
382992.33
38^537.07
382082.81
381629.57
381177*33
380726.09
380275.85
379826.61
379378.35
378931.09
378484.81
378035^,^1
377S9S'^9
377151.85
37^6709,47
376268,07
375827.63
375^388.15
37^9^9. 6^
3745:12.07
96607.62 j 3 74075 .46
96600.101373639,80
9659^.58! 373105.08
Secans
399391.9^
98944-^'.i
98496.54
98049.91
97604.31
97lf9.7f
967x6.21
96273.69
95832.19
9J3^l*7i
9495».»4
9^U3'79
94076.33
93639-88
93104^
9^769*97
9^336*Sl
91904.03
91471.54
91042.03
90612,50
90183.95
^97S6.37
893i«.76
88904«il
88479.43
88055.70
87632.93
87211.12
86790.25
86370.33
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9.92$94i6
9.985908^
9^995 ^761
9.9858434
9*9858106
^•9857777
9*985744^
9.9857119
9.9856790
9.9856460
9.9856129
9.98557^8
8.9855467
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9.9854803
9.9854471
9.9854138
9.9853805
9.9853471
9.9853138
9*9852803
9.9851468
9.9852133
9*9851798
9.9851461
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9.9850789
9.9850452
9.9850114
9:9849776
9.9.841^438
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[0.587341^
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:o.5 863007
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10.5800987
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7
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16
17
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21
22
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25PIO.OO
25^^38.10
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267^4.^2
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26857.28
26888.47
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26^2.07
27013.28
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103682.75
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103707.57
103715.87
103724.17
103732.49
103740.82
103749.15
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9.4129962
9.4134^74
94I3938I
9.4144082
j?4i4»778
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9.4167506
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9.4223176
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9.4232380
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9.44003^3
9.4405*95
94410222
94415145
9.4420062
9-44*45^75
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63460.64
63047.71
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386370.33
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8jrii6.ii
84700.0J
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838'70.yx
834^7.13
83044.67
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9.9849438
9.9849099
9.9841^760
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9-9848081
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26751.87
16779 '^9
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2683M4
26863 .p6
268^1.^8
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27032.04
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27iiéî.o5
27144.04
27172.04
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177^3-78
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27826.46
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9.4268988
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9.4278089
9.4282631
9.4*87169
9.4291 701
9.4296228
9.4300750
9.4305*67
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362417.88
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361694-90
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256x05 .95>
1JÎ930.47
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9-96S6iSi
9.96SS6io
9*96$ S106
9.9^545 82
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9*9653SSi
9.9^53<»^
9.965248a
9.9651951
9.96514 ^6
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9-9650371
9.96498^»
9^6^93H
9.9648785
9.9648256
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9^96^7195
9'964666S
9'96^ill
9.9645602
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P.9644537
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9.9643470
9.i>642937
9.9642402
9.9641868
9.9640797
9.964026I
Lûg/TatL
[0.3827757
[0.382419^
[0.3820615
[0.3817047
[0.3813481
[0.380^17
[0.380635'$'
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0.376377J
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16
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3979^^6
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10
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39811.^
39848.23
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4^44^*4^
42^.81^
4wj'ï^.f^
4*f^-«7
42^r^éftif
4*72*«3^
4^6.79
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42:9^3.39
42997'9f
43032.52
43066.80
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43101.29
43I3^75^
43170^
43^4.81
43^35^.33
43273.86
43308.40
4334»«5*
43377.^1
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43412.08
43446.66
43481.24
13 Grad.
Secans
08636.04
C2Î649'^
0(^62.89
081^76.34
68689.7^
08^^03.26
0871 6.7f
087)0.24
08743 '7^
o87î7.*7
Ô8770.80
08784.3J
0Î797'9*
o88ri.48
6^825.06
08838.66
o885r2.27
0886^.89
08879.^*
08893.17
08906.83
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08)^4.18
08947.88
069^1.^9
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08989.04
09002.79
o9oi6.jy
09030.32
09044.11
9.S9i^^
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9'f9^7é9^
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9'$936i9^
9-S939StS
9*5 9^1 13
9'S9^S469
9.S9^M^i
9'S9Si37S
9.î9y43"
9;W7i«8
9'.J96o2i2
9.5'963iT4
9.J966093
9>19è9oio
9'S97i96l
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9.59778x7
9.Î986W4
9i^9^3é79
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9*S9^9^^i
9.S99Sil7
9.J9P8271
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9.6004090
9^096997
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9'.628£03i
^.^289048
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9-.6292JÎ3
9-.62960J7
' 9.6i99jry8
9.63030J8
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9.6310052
9-6313545
9.6317037
9.6320527
9.6^3*4015
9'.63a75oi
9^633098^
9.633 4îfé«\
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9.6^41426
9.6342fi?oj
9.^34^*57^^
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9.^5*^? II
9.éi^90
9.6*36^x57
^.65657»*
9.6369185
9.6372646
9.6376106
9.6375^563
9.6J 83019
s
i
H
n
tftf Grad
Sinus
9ioS0.^9 23^^8^.14
5^x63^.12
9^^7'U
t
47
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44
4»
41
40
3s
57
91991.$ 6
9^970.73
919^9.31
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»3« 5^4.83
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a3yoi4>8i
,2348iy.f5»
i3463^8^
.*i444^-y*
5^i^*4f5^
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31
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9iyz9.i9
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231825.06
231^40.76
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231270.^1
231086.36
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230por.o6
230718^.01
*3oy34»xo
2303^0.64
^1717.60 1230167.32
91706.01 ;22P5?84.2J
Secans
2ff4c>y^8*
-fcfa
25'jri^.or
25505^6.80
25'48S2.84
2î47o^.iJ
»W35.7X
254362.5^
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a!f3328.83
2^13^17.44
215*^86.30
2^28^1^^!
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2^2644.7^
2524744P
252304.261
252134:3'^
iSi^4^7S
2517^-37
251626^4,
^HS74S
25128Ï.71
25112Û.32
250^52.18
250784a8
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^.^640 261
9*96397^4
9-96391^7
9^3^So
^.^638112
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9*9636^6
9'963S9S7
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9-9619994
9-9619^9
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9-Sf6t&j\9
9.96l'ei7i
9.9^f6%4
9.961^076
9.96x^^17
9*961^97^
Lûg.Tan.
T0.372I48I
10:3717969
10.3714460 '
10.3710^2
10.3707447
10.3703^43
10.3700441
< 1 un
10.36^6^42
10.36^3444
io.^8i>^4S
10.3686455
jo.3^82^63
ià^i947l
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10.36724^^
10.366^1 f
'10.36^513*
10.3662052
10.3658574
10.365 505^7
10.3651622
10.3648150!
10.364467^]
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10.3616^1
9
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38
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47
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35>^i.î8
3Pyi8.ij
4QO08.24
40034.^
40061 .f 6
4Z088.ZI
40114.8e
40141.^0
40168.14
401^4-78
40111.41
40148.04
40174.67
40301.IJ;
40317.p1
403 y 4-^3
40381.14
40407.7^
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40460.P6
40487.^^
40^14.16
40^40.7^
. 405^^7-34
405^3 •P3
40610.^
40647.09
Tang.
43481.14
43^^.83
43îîo^43
43 î 8^.04
43619.66
43654.*P
43<^88.93
43713-^8
43758^3
437P1.89
43817.^6
43861,14
438p^.P3
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43P3i'^3
43P^^-34
44001.06
4403 y. 78
44O7O.fl
44ioî-iy
44140.00
44i74«76
44^op.r3
44144.31
44179.10
44313.P0
44348.71
44383.T3
4441 8.3 f
444^3.18
44488.01
40673.661 445»».87
Secans
09044.11
09057.91
09071.71
o9o8^r4
09099.38
09113.23
09117.09
09140.97
091^4.86
09168.76
09181.67
09196.S9
09110.5:3
09114.48
09138.45
09151.43
09166.41
09180.41
09194-44
0930847
09311.51
09336.56
09350.63
09364.71
09378.80
o939*.pi
IPP407.03
0P41Ï.16
0943T30
0944P..4^
09463.63
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9.6006997
9.6009901
9.6011803
9.6015703
9.6018600
9.^011495
9.6014388
9.6017178
9.6030166
9.6033051
9*6osS9S6
9.6038817
9.6041696
9.6044573
9.6047448
9.6050310
9.6053190
9.6056057
9.6058913
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9.6061786
9.6064647
9.6067506
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9.6070361
9.6073 116
9.6076068
9.6078918
9.6081765
9.6084611
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9.6087454
9.6090194
P.6093133
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9.6383015^
9'6sU^73
9'6}999ii
9>és93S7S
9.6396813
9.6400169
9.6403714
9.6407156
9.6410597
9.^414036
9.6417473
9.6410908
9.6414341
9.6417773
9.6431103
9.6434631
9.6438057
9k644i48r
9.6444903r
9.6448314
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9.645516a
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9.645857^
9.6461988
9.64654OO
9.646881a
9^6471*17
9.6475614
9.6479018
9.6481431
9^85831
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■*-^M
9
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II
io
19
I8
17
lé
ly
13
12
II
10
9
7
4
J
2
I
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^1706.01
^1682.80
pr^7i.i8
916S9-SS
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9ï6$6.Z7
9i6ij^,6i
91611,96
91601.^0
915^9^6^
9iS77*9S
9iS66.x6
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22pp84.aj
22^801.43
22p6i8.8j
22P436.J1
22^2^4.42
22^072.57
2288po.p<!;
22870^.^^
228528.46
228j47.y8
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915^9'^Z
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91^95-96
P1484.22
P1472.47
P1460.71
pi448.py
piiB7.i8
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P1413.61
91401.81
P13P0.00
91378.XP
9i^66j^7
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228166.^3
227^86.53
227806.36
227626.43
227446.74
227267.29
227088.07
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226^51.84
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226ipf.53
226017.73
225840.16
225662.^
225485.7^
225308.85
225132.21
224P55.80
22477P.62
224603.68
Secans
250784.28
250616.63
25044P.23
250282.07
250115.15
24PP48.47
24P782.04
145^615.86
24p44p.p1
24P284.2.1
24P118.74
348^î3-5*
248788.54
248623 .80
»4845i>.i^
2482P5.03
248131.00
247P67.2I
24780^,66
247640.34
247477.26
247314.42
24715 i.8r
246P8P43
246827.2P
246665.38
246503.71
246342.27
246181.06
246020.08
i458yp.33
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■^ " - 'I- I II ■
P.i?623P78
P.P623428
9*9^ii%7%
P.P622328
P.P621777
P.P621226
P.P620674
P.p620122
9-96195^9
P.p6ipoi6
P.P618463
9-9617909
9-96ï7i5S
p.p6i68oo
9*96i6i^S
9'96i$6%9
9.961S13S
9.961 J^S 76
P.P614020
P.P6I3463
p.p6i2p04
P.p6i»346
P.P6II787
p.p6lI228
P.P6I0668
p.p6ioio8
P.^6op548
p.p6o8p87
P.P608426
p.96Q7i64
P.P607302
[o.36i6p8r
[0.36T3527
[o.36ioo7f
[o.36o662f
1 0.3 603 177
10.35PP731
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10.3JP2844
to.358p4oj
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fO'3J756ri
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tO«3572228
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8
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14
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17
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19
XI
22
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24
■^7
28
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40673.66
40700.23
40726.80
40753-37
40779.^3
40806.4^
40833.05
4o85:p.6o{ 44767.08
Tang-
44557.73
44592.60
44^62.37
44^i?7.»7
44731.I7
X4 Grad.
Secans
109463.6]
ioj^477«8i
109492.01
109506.22
_EK.
40886.1^
40912.69
4093 9 A3
40965.77
40992.30
41018.83
41045.36
41071.89
44802.00
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44871.87
44906.82
44941.78
41098.41
41124.93
4II5I.44
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45011.73
45046.72
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109548*^*
109563*18
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109591.74
109606.04
109620.36
10963^.68
109^49.02
109663.37
109677.74
4508172
45116.73
45151.74
41177.95 4518^.76
41204.46
41230.96 45*5^.83
41257^6
41*83.95
41310.44
4î33^-^3
41363.42
41389.90
45221.79
4^291.88
453*^.^4
45362.01
109691.11
109706.51
I0^20«9I
109735.33
109749.7^
109764.20
45397.09
45432.18
45^467.28
45502.39
109778.6^
109793.13
109807.61
41416.38
41442.85145137.5 1
414^9.3»
109822 .II
109836.62
169851.14
109865.68
109880.23
4557^.^4 Î09894.79
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9J^im
9^9^9i9
9.6098863
9.6ioi6}5
9.6XP4465
9^x07^93
9.6XX9SX8
9.61x1941
9.^1x576*
9.6ii?s8p
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9.6513113
9.6526503
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9.6131641
9^13544^
9.6138250
9*614105 X
9.6143850
9.6519881
9.6533*57
9^536631
9.6540004
9.6543375
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9.6x46647
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9*6x51134
9.6x55014
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9.6x60599
9.6163J81
9.6166x64
9.6I68944
9*6x7X7îX
9,6174496
9.6177270
9.655oii>
9-6553477
9.6556841
9,65^0*04
9.65635^
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9.6573^3^
9.6S769^9
9.6580341
9.6583^^»
9.6587O4Î
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51
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44
43
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41
40
39
38
37
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35
54
33
^5 Grad.
^1283.41
91ZS9M
Sinus I Tangt | Secans
M5 85^.33
M5538.53
M537M
5»i354-54
— »^^— «OHM»
Pi34*-7i
^1330.87
^131^.0»
**37*7.38
»i355^*8o
"3378.45
2*3*04.33
123030.43
9123^.84
91223.^3
^1212.01
^1200.08
5»i 188.14
^1176.20
pu 64.25
9lif^A9
5^x140.32
^1x28.35
PII16.37
pii04»38
pxop2.38
91080.38
pio68%^37
9JCSe*$S
P1044.32
91032.28
91020.24
91008.19
224603.68
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224427.96
224252.47
224077.21
222856.7^
222683.31
2225x0.09
222337.09
2»2l64.32
221991*77
221819.44
221647.33
221475.45
221303.79
221132.34
220961.12
n i III
m—
245218.65
245059,05
*^99*é%
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2445 8x^63
244422.94
244264«4S
244106.24
243948.23
24379o.4r
243632.89
»43475.55
«i«^— ^ Il
MÎ3 18.44
»43 1^1-55
243004.89
220790.12
2206x9.34
220448*78
220278^3
220x08.31
219^38.40
242848.44
242692.22
242536.22
242380^^
242224.88
242069.54
24I9I4.42
241759.52
241604.84'
3*
31
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219768.7X
219599.13
241450.38
241296.X3
241142.10
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9.^607302
9>9^oé7S9
9.9606176
9.9605612
9.9605048
9.51604484
9.96039x9
9'9éo}3S^
9.9602788
9.9602222
9.960x655
9.9^to88
9*9600520
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10.3476875
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10.342972!
10.34263K
xo^423Qx:
xo.34i96ri
10.341^36!
10.3412961
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33
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34
3^
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37
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40
41
41
43
44
4Î
46
•47
48
;4P
II
.fi
■J4
^1
S6
S7
>6ç
Sinus
4146^-31
4I45>J.7P
415^4^.7»
4157^.18
41661.63
4iéi8*o&
41680.^7
4i707*4i
41733-85
41760.X8
41786.71
Tang-
4157^*64
45^7-77
45641.^1
4^^78.06
45713-11
45748.3P
45783.^7
45818.76
458^3-^
4588^.17
41813.13
4183^.55
4ï86ç.^7
41 85^1.3^
41^18.80
4iS4y-il
4IP7I.6I
4i^y8.oi
41014.41
41050.80
41077.IP
41103.58
4111^.^
41156.34
^ 42.181.71
4110^.0^
41135.4^
41161 .$3
45^4-3^
45^^.61
45^^4-86
46030.11
41^065.37
46100.64
46135.^1
46171.1^
46106.48
46x41.78
46177*0^
4^3<^*4>i
46347.76
463 83. XI
4641846
4^453**
4648^.1^
46514.57
4^55^.^
465^5.36
46630.77
14 Grad.
Secans
09^9^79
09909-16
099^$ '9$
0^^38.55
o^P53'i7
09967*79
0^^81.43
09997^9
0011.76
0016.44
0041 .13
0055.84
0070.56
0085.19
0100.04
0114.80
OI1M7
0144.36
0159.16
0173.97
0188.79
0103.63
0118.49
o*33-35
0148.13
0163.13
0178.03
^9i**9i
0307.89
0311.83
OJ37.79
Log.Sin,
9.6177170
9.6180041
9-6181809
9.6185576
9'6i8834i
9.61 91 103
9*6193864
9.6196611
9 '619917^
9.6101131
9.6104884
9.6107634
9.6110381
9.6113 117
9.6115871
9.6118611
9.^111351
9.6114088
9.6116814
9.6119557
9«6i3ix87
9.6135016
9.6137743
9.6140467
9.6143x90
9.614591 1
9.6H8629
9.615x346
9.6154060
^.6156771
I9.615948J
., '
LogHTôn
9.6587041
9^90l%7
9'6S9373J
9.6S9707^
.■■■■ ■ ■!
9.6660418
9.660375 rf
9.6607097
^.66104^4
9.6613769
9.66i7i03r
9.6610434
9.66IJ765
9.6617093
9.6630410
9.6633745-
9.6637O69J
946^40391
9.66437X1
9.6647030
9.6650346
9A6Sl66%
9MS697S
9.6660188
9'666^S9^
9^6666907
9.66701x4
9*667 SSi9
9*6676%%^
9^69oix6
9.^68341^
9.6686715 t
I
9
18
i7
i6
22
21
20
18
17
Ï4
II
XI
10
9
7
^5 Grad.
Sinus
90996a^
909^jiy6
9097^9^
909S9^90
50^47.81
909^S*7l
9091$ •^i
90911, $0
9oZ99-$^
9o9S7'^S
90^t'97
^850.82
^838.^^
9o%z6j^9
^814.32
^8oi.i4
907%9*91
^0777-75
S
4
3
^7^J-f4
^07«-35
507i8.88
^071^.^4
^70440
90691^$
90679^^9
90667,6%
Tang.
%19^9*97
2i^26o.j?3
21^^2.10
218^2349
21 875 J ,10
21858^.91
218418.94
2l82f|.I9
218083*64
22791^.31
217749.20
217582^9
"74iy-fp
21 7249.11
217082.83
116916.77
2167^0.91
2i6jr8f.27
21^419.83
Secans
«■*
241 142.10
240988.29
240834.69
240681.32
240^28.15^
240371*^0
240222.47
24OO69.9T
2399X7*64
»3^7^^.T1
2162^4.60
216089.^8
2iJ9»4-7^
2ijr76o.iy
*Iîf9^7jr
2if43i,56
* 906SS.3I
i 90643.07
ol9P^3Q.78
%1S%6747
21^103.^8
214^40,20
1x477^.83
214613,66
, 2144^0.69
139613.67
239462.01
»5^3ïO'1^5'
i59iS9*3i
239008.28
2388^7*4^
2387O6.8J
2384o6.2f
2382^6^7
238106.50
^^379$6.93
237807.58
»37^r8.43
^$7^09^9
237212.22
1370^3.^
13^^15^.78
436767.87
236620.16
Log.Sin.
^■i— — »
9.95^0229
M$996SS
9.9S^9077
9.9^88500
9.9587913
5>.5>58734J
9-95^767
9.9586188
9.9585609
9.9585030
9.9^84450
9.9583 8^P
9.9583288
9.9582707
9.9^82i2f
9.9581543
9>95^9éi
9.^^80378
9'9S7979^
^.9179110
9.9^78626
9.9578041
9-9S77AS6
9.^57^870
9.9jr7^l84
9'9S75697
9.9^7^110
9.957451 1
9^7^934
P.957334^
9>9S7^7S7
XO.34I296O
10.3409613
10.3406267
10.3402924
10.3399582
10.3396242
10.3392903
10.338^566
10.3386231
10.3381897
10.33795^^^
10.3376235
10.3371907
10.3349580
10.3366255
10.3362931
■ »«
10.335^9609
10.3356289
10.3352970
10.334^54
10.3346338
10.3343025
10.3339712
io»3336402
ï^*3333o^3.
JO.3 319786
10.3326481
10.3323177
10.3319874
10.3316574
10.3313271
G 3
n
M*
I
%
4
6
8
10
II
t%
14
if
tr
ts
19
ftl
»9
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^5 Grad.
Sintts
4i2'6i.8j
4XZ88.I9
4iîi4-ff
41340.^
4*3^7^f
4»3P3'^
4t4ip^
4M4^««d
4X47i.éx
4t49K.9r
4trif.t8
4*yîri^i
4*T77.^
4X^64.zf
41630.5:^
42éfé.S7
4^^83.18
4»70P»49
4»75f*7^
4i7éz.09
4t788*3S
41814.^7
4*840.9îr
49t8^7.2'3
4x8p3.rr
4*9i9-r9
4xp4^.9é
4497^.33*
-*— •
4*998.r9
^OM.8r
Tang.
46630.77
4é^i^6.ip
46701.6%
46737^6
4677^.^1
4^^.P7
4^843.^
46878.^
46^14.38
46949.88
4^98^.39
47OZO.90
470f6.4^
47091.96
47l»7-fï
47163.06
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47198.63
47*34«*0
47*^9.78
4730^.38
47540.98
4737^.^9
474u.1i
47447.8f
47485.49
47^19.14
47rf4-8l
475'5».48
476i6«t6
47661 .8f
4îofï.n 47697*^
Secans
IX0337-79
1103^1.77
110367.7^
110381.7^
1103^.77
I 10411.79
110417.83
110441.89
Ii04î7.9f
110473.03
1 10488. 13
xiO]i03«i4
110^18.36
■WM
110^33 .49
110^48.64
noir 63 .80
110^78.98
II0194-17
110609.3^7
110614.58
110639.81
Iio6ff.06
X 10670.31
iio68jr.58
110700.87
Ii07t6.i6
110751.47
110746.80
M*MMk
1 10761.14
110777.49
ïX^9*.8f
9.6M94^
9.6161 191
9.6164897
9.6167601
9-6170303
9.6173003
9.6175^701
9.6178397
9.6181090
9.6183781
9.6186471
9.6189160
9.6191845
9.6I94TI9
9.61971 II
9.6199890
9.6301^68
9.6305143
9.6307917
9.670^774
9.6713060
9.671 634^
9.6719618
9.6711910
9.6716190
■«^
9.6310589
9.6313158
9.6315916
9.63i85'9i
9.631115^
9.6313916
!•*■
9.63*6^7^
9.^3*^2^55
9.6331889
9.63345:41
9.6337194
^•^339844
Lûg.Tan
9.668671?
9.6690013
f. 6693 3.19
9.6696613
9.6699^6
9.6703197
9.6706486
9.6719468
9.673 I74f
9.6736010
9.6739194
9.6741566
9.6745836
9.6749105
9^^755638
9.<^7ir896i
9.676^165
9.6.765416
9.6768686
9.6771944
9.677f»or
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9.6778456
9.67^X7^
9.61784961
s
60
T8
17
7^
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47
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4f
44
43
4»
41
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38
37
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3y
34
33
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Sinus
90610.7%
^yp3.8^
pof8i.î4
90S69'ti
90SS6M
Tang,
114450.6^
^T44-Î4
Poyip.85
pofo7^5
^481.71
^470.31
P04Î7.^2
p044y»Tl
^433.10
P04&0.68
^408.2^
^9^8^
^83^8
90^0.9^
P0358.47
^34^«o6
5^J3-«
^32i«6f
po3o«.f6
90%96,ôé
^0283.^6
<^27i.of
fOtJ«.J3
^4 Grad,
Secans
236^20.16
4287.^3
4liy-37
3^53.01
3800.8^
3^38.8^
3477.^4
33^5'.^^
3ir4.»3
ip^.o8
2832.13
2^71.^7
2]rio,Sx
2^6^7^.6s
î^3^3M.3y
236178.2^
*3^3ï'3^i
*3r 884.67'
»3y738.i8
*3J^i>ï-8P
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^$S^99*9^
23^0.46
21^0.30
2030^34
1870.57
1711.01
iTJi.^4
13MT4-X4
2:3^008.75:
X3 4863 .47
j»347i8.38
1*34^73.4^
234428.80
234284.31
234140.02
^l^99S-9l
13^2.46
1x33-48
1074.70
0916,11
<*7f7.7l
0199*U
0441.50
0283.6^
6126.07
^0996%j6\
10981 t^o
^>^54-3^
233^52.03
233708.33
133564.82
233421.52
233278.40
233135.48
232992.76
232850.23
131707.90
13»T^J.75
2324x3.81
Log.Sin.
9'9S7^7$7
9.95711^8
9>9S7JS7^
P.PÎ70988
9'9S7oi97
^.95^69806
P.9569215
9.9568623
9.9568030
9.9167/^17
9.9^66844
9'9S66iSo
9'9i6s6s6
9'9S6so6i
9-916^6
9.95^3870
9.9)63274
9.9161672
9.9562081
9.9^61483
9.95^^0886
9.95^0287
9.9119699
9.91190^9
9.9IIM90
9.9557890
P.9557189
9.^556688
9.9II60Î7
9.911U91
9>91Unz
G 4
0.3313275
0.3309977
0.3306681
0.3303387
I
0.3300094'
0.3296803 i
0.3293514;
0.3290226'
0.3286940
0.3283655
0.3280372
0.3277090 j
0.3273810;
0.3270532
0.3267255
0.3263980
0.3260706
0.3157434
0.3254164
0.3250895
0.3247628
0.3244362
0,3241097
0.3^37835
o.3i345'74
©.3 231 314
0.3228056
0.3x24799
0.3121544
0.321 8291
0.31150^9
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TA
$9
4»
4Î
44
4r
4<?
47
f
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f7
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S9
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Sinus Tang.
43077.3^ 47733 -i^
43103.61 477^8.^9
431x^.86 47804.7*
» I » ■ t I II —
431^6.10 47840.46
43181.34 47«7é.ii
43^08.^7 47Pri.p7
43134-80 47^47.74
43161.03147^83.^1
43187.16 4801^.51
,433^3-48 ;45ôjrrz
4333^-70
4336^^I
433^1-1*
43418.33
43444.^3
—
43470.73 48170.14
434P^.pi 48306.01
43^13'" 48341 .8p
435^45^-30 48377.78
480P0.P3
481*5.7^
48161.^8
48158.41
48134.17
43f7f^8
43601.66
43^*7.84
4365^4-01
43680.18
43706.34
4373*Jro
437T8.66
43784.81
43810.57
43837.1*
48413.68
4844M9
4848^.^1
48ni.4r
48W4^
48^53-34
48<i9.3i
4866^l8
48701^6
48737.16
48773.*^
Secans
Ii075i.8f
IÔ808.13
10S13.63
10835.03
108^4.4^
vio%69S9
io885'.33
10500.75
10516.17
10531.76
10547.16
10561.77
10578.30
10553.85
tioo5wfi
11014.58
kéfv
11040.56
IIO56.I6
ITO7I.77
11087.40
II 103 .04
IIII8.65
11134.36
III5Q.O4
III65.73
1118144
Iti57»i6
IXIII.50
IIU8.65
IÏM4-4*
ii^6o«i5
Lûg*Sin,
^^6335844
5.6341451
5.6345137
5.6347780
5.6350411
5.6353061
9'6iSS699
5».6358J35
5.6360565
5.6363601
5.6366131
9.6^69%$9
5.6371484
5.6374108
5.6376731
^•6375351
5.6381565
5.63845^8^
5.6387I9P
5.63S58I1
9^i9^4Z2,
5.635^030
9^397637
5.6400141
546401844
5.^40f44r
5*^408044
5^6410640
5*6413135
5*6415818
^.6418419
Log.Tém
5.6784561
5.^788x11
^.6751460
^.67^4708
9*67979^1
5.680II58
5.6804440
5.6B07681
5*68i05&i
5.6814166
5.6817356
5.6810631
5.6813 Z6%
5.6817058
5.6830318
9>69^SfS7
5.6836785
5.684001 1
9.684313^
5.6846455
5.6845681
5.6851501
5*^856110
9MS9l^i
9'^^%SSi
5.68657^
5.6868581
5.6871151
5.6875402
5.68786XX
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Î3
21
ZO
19
.18
17
lé
IS
ï3
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II
lo
9
7
7
4
2
1
O
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Sinus
il I ■ ■ ■ iM^M»
P025r8.T3
90246.00
P0233.47
90220.^3
^208.38
9019$. îz
^183.2^
90I70.6Z
90iS^Ao
9oiJ^^
90ï$z.9î
P0120.31
^0107.70
poopf.ôS
90o8x.4^
9006^,82
9CJ057.ia
90044.^3
900^ 1.87
5»oip.2i
>ooo6.îr4
89^93. 8é
8^y8i.i7
8^68^8
8ppyy.78
89^43.07
89^30.3^
8^i?i7.^2
8jp9C54.8^
8pSp2.i^
8987^.40
Tang.
20^6^4.36
2'95»4P7.5i
20^340.84
2opi 84.37
20^28.0P
208872.00
208716.10
208560.39
208404.É6
208249.53
208094.38
i07^3^*4*
207784.65
207630.07
20747^.^7
207321.46
207167.43
207013.59
206859.93
206706.46
206553.18
206400.08
206247.16
20609442
*0594i.87
205789.50
105637.32
2054S5.31
i05333'45»
205181.84
205030.38
Secans
— ■»
232282.05
232140.49
231857.94
231716.95
^i 157^.15
»3 143^*^4
»3^*^5^-lJ
23ii54.5>o
231014.86
230875.01
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»3o^9^-88
I I m — — .fc
230456.60
230317.51
^30178.60
230039.88
229901.34
229762.99
229624.83
229486.85
i»5'34P.o6
229211.45
229074.03
228936.79
228799.74
228662.86
228526.18
228389.67
228253.34
9.955M<^9
9.9551864
9.955 1*59
Log.Sin.
9*9554882
9.9554*80
9.9SSf676
9.9553073
9-95506^3
9.95^0047
9^95^441
9.9548834
9.9548127
9.9147^19
9'9S470U
9.954^40*
9.9545^793
9.954^184
9-9SW74
9'9$Ai96$
9.9537833
9.9537118
228ii7.?lot 19.953^^02;
9.95433^1
9.9541741
9.9541119
9.9541^7
9.9540904
9.9540191
9 '913 9677
9.9539063
9.9538448
10.3215039
[O.32II789
[O.3 208540
[0.3205292
[ 0.3 202047
[O.3 198803
[0.31955^0
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rO.3192318
[ 0.3 189079
[O.3 185840
[O.3 182604
10,31793^8
^0.317^13?
[O.3I729Ô2
[O.3 169672
[O.3 166443
[O.3I632I5
[O.3I 59989
[O.3I56764
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[O.3I5O3I9
f 0.3 147099
tO.3143880
[ 0.3 140662
tO.3 137447
[0.3134232
[0,3131019
[0,3127808
[O.3 124598
[0.3121389^
[o.j;^i8i8z
SB
9
I
1
3
Sinus
40700.13
40716.80
40753.37
41 ^79*91
40806^.4^
4o8^^.éo
4o88é.if
«40^1 2.6^
S
6
7
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9
10
II
IX
M
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16
17
18
19
20
XI
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24
28
19
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44^22.87
44^57.73
44592.60
44627.48
4093 9 A3
405^65.77
40^92.30
44662.37
44^^7.i7
4473^>I7
44767.08
44802.00
44836.93
X4 Grad.
Secans
IQ94^3.6|
109477-81
10^492.01
109506.22
iJES.
44871.87
44906.82
44941.78
41018.83
41045.36
41071.89
41098.41
41124.93
41151.44
41177.95
41204.46
41230.96
4497^-75
45011.73
4f 0146*72
45081.72
4511^.73
4515X.74
41257^6
4U83 .95
41310.44
4î33^-^3
41363.42
41389.90
45186.76
45*2.1 -79
4J256.83
45291.88
45326.94
45362.01
1095*0.44
io9534»^7
109548.9»
1095^3*18
109577.4^
109591.74
109606.04
109620.36
10963^4.68
109649*02
109663.37
109677.74
109692.11
109706.51
1097*0.91
^
45397.09
45432.18
45467.18
41416.38 45502.39
41442.85 [45537.51
45572.64
30J 41469.
3*
109735.33
109749.7^
109764.20
109778.6*
109793 -13
Ip98p7.6x
109822 .II
IQ9836.62
I6985I.I4
I09S65.68
109880.23
109894.79
■ I . < 1 II ■ ■ . I .
Lûg.Sin.
9.6993133
9.60959^9
9.60989^3
9.6iox6}5
9.6194465
9.6107293
9.6il9Sl8
9.6112941
9.^11576^
9.6il?î8p
9.6485831
9.6489*3«
9^49X^%9
9.649601}
9^994^7
9.650180^
9.6506x^9
9.650*587
9.65ii^4
9.651^359
9.6I2Î397 9.651974»
9.61 2421 I
9w6i 27923
9.6129833
9.6132641
9.6135446
9.6138250
9*6141051
9.6143850
9.6523123
9.65*6503
9.6529881
9.6533*^7
9.6536631
9.6146647
9.6149441
9«6l52*34
9.6540004
9.6543375
^.6546744
'9.6550112
9.6553477
9.6556841
9.61559*4
9..615781*
9.6169598
9.6163J82
9.6166164
9.6168944
9.61717*1
9,6174496
9.6569&04
9.6563564
9.65669^3
^.6570280
9.6573636
9*6S76999
9.6580341
9.65836^2
9.6177270I9.658704Ï
E
Ti>
^7
U
lï
IL
jp
49
î!
47
4^
4^
44
43
4»
41
40
11
ïs
34
33
3*
30
^5 Grad.
Sinus
9t3S4'S4
il I ' I»
yi34*-7i
^1307.16
9l^9S^9
.^1183 .41
9l^7l*S4
9ltS9.6S
9l^47*7S
Tang.
224603 .68
224427.^6
2^2f2.47
214077.21
223i?0».l8
223727.38
223552.80
223378.45
223204.33
223030.43
^1135.84
91X23.^3
PI2I2.0I
^1200.08
^1188.14
^1176,20
^1164.25
9lii%A9
pi 140.3 2
^1128.35
Pi 11^.37
pii04«38
^10^2.3 8
^1080.38
pio6&«37
9^0Sé.SS
P1044.32
91032.28
91020.24
91008.19
90996.1$
222683.31
222510.09
222337.09
2^2164.32
221991.77
Secans
Mî 859.33
245698.82
245378.48
245218.65
245059.05
244899.68
244740.54
24458X463
244422.94
244264^18
244106.24
243948.23
221819.44
WI647.33
221475.45
221303.79
221132.34
^43790.4/f
2436^2.89
^^47S*SS
•— •^••••^^•.^
M33 18.44
*43i^i.5f
243004.89
242848.44
14169%,%^
110961. iz 242536.22
220790.12
220619.34
220448*78
220278.43
220108.31
219938.40
219768.71
2195^9.13
2l94*P-^7
242380^^4
242224.88
242069.54
24I9I4.4X
241759.5»
241604.84'
241450.38
24i296.jr3
2411 42.10
9.9607302
«***■
9>96oé739
9.9606176
9'96of6ii
9.96^05048
9.9^84
9»96o$9l9
55603354
9.9^1788
9.9^02222
9.9^01655
9.9^to88
9*9^00520
9*9S999Si
9'9S99S^
1^.9^98815
9^^9814^
9*9^97676
9.9S97106
9^9S96SSS
9-9S^96^
9'9S9S39S
9 '9194^^1
9.9^94*48
9>9f9$67S
9>'9S9ilo%
9*919%St^
9'919i9$4
9'9S9l$^
9*9$9<^^
9'9S90tZ9
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10.35141^
10.351077
ip-3^0737
10,350397
10.350058
10.349719
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10.349041
IO.3487OA
10.348364
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10.348025
10.347687
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10.347011
10.346674
10.346336
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10.34T3M
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10.344652
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10.343307
10.342972
to.342636
10.342301
10.341965
10.34*630
19.341 296<
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34
3f
J7
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40
41
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43
44
45
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47
48
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75
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4461 9.7S
4464^ .81
44^71.84
^97M
447^3-88
4474P.PO
44775^.91
44801.^1
448*7.^1
448^.9*
44879.9»
449of.9ï
44931 «90
4^8y8.ié
4^894.49
499jo.fe
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449J7»89
44983 -«7
45009.85:
4^03 y -8»
4îoéi.79
41087.76
4f"3.7i
45139.^8
45I6^63
4Ti9i.f8
4^*17-^3
4?H3'47
41*69.41
45:W.31
41311.28
41347."
45^373.13
4f 399.01 1
10111.66
10149.06
10181.47
10211.8^
10x18.31
lO»^4.76
10331. II
10367.67
10404*11
10440.63
5:0477.13
10113.63
10110.11
10186.68
106x3 .11
10619.77
ro696.33
10731,^
1076^.48
10806.07
1084X.67
10875.18
10911.91
1091*. 14
i(J Grad.
Secans
II 1740.04
1716*1
177A.48
17^8.71
1804.98
1 811 .11
1837.13.
1813.83
1870.14
1886.47
1901.81
1919.16
I93f.l3
191 1. 91
1968.31
1984.71
2001.11
1017^9
1034.01
loio.ix
^7.00
Î083.I0
IIOQJOI
1116.13
*i33 .07
«49.63
1166.10
1181.78
M99.38
1116.00
1131.61
9M95^7^
9.6^97^
9.6100338
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9.6S0S$9S
9.6107910
p.61 10444
9.6111966
9.6H1486
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9-6110111
9.6113031
9.6111148
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9.6130168^
9.6133(?71
9.6131181
9.613 8Q84
p.6140186
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9.6141184
9*6148081
9.«llai71
9.6113068
9>6SS1SS9
9.6118048
9.6l'6ol36
9*61630x1
^■^••1— ^i«aiii^»aiiaa
9.6I6ÎIOI
P.6I67987
^.6170468
Lâg.Tan
9.6^77363
9'69^z6
9.6983^8^
^•6^86847
9.6990006
9.6993164
9^996%if>
9.6999474
9*7001618
9.7001780
5.7008^30
5.7011080
|9.70îl»i7
5.7018374
5.70x1119
5.70x4663
9.70x7801
9^7^30546
5*703 4Ï386
9.7037*if
5.7040361
9.7«>43497
^-^—i ■ » Il ■ » »
9.7046631
5*7049761
9.701x897
5.7016017
9.70^5116
5.7061184
5.7065419
9.7068131
9.7071619 1
r
9
E
*7
lé
10
I8
17
lé
14
II
II
10
s
^3 Grad.
Shius I Tang.
8^480.4^
8^4^4.46
8P44i-4f
8^428.44
8^4ïf-4*
8^40H^
8^8^.36
85>3 7^.31
8^3^3-17
893Jaii
85^37-14
8^3 14.0e
8^310.^8
8^1^7.8^
89184.79
?9l7l-éy
8yi5r8«f8
100^68.^7
100421.9^
100C77.IO
100131,41
199840.^6
^ 9969s '19
89141.46
89131.33
89119*10
89106.0e
^191.91
^179 '7S
^9l66.S9
4 891^3^1
3 89140.14
1 89ii7X>l
89ii3,8f
o| 89100.6 j
i^^fo.38
199401^14
1991^.87
1991x6.37
X98971.04
198817.87
198683.87
198^40^3
19839^.36
1981^1.86
198209.^1
WPé6.3f
197813.34
I97é8o.fo
i^7y37>8i
I97»ri.96
197110.77
I9é9é8.74
196816.88
I9é68f.i8
l9é5'43-64
196401.17
196161. of
Secans
114x1^.84
ii398îr.i7
ii3'8l4.67
113714.37
113194.19
113464.10
113334.38
113^^04.74
113071.16
111947 >91
111816.81
111687.83
111119.03
111430.39
111301.91
111173.61
111041.48
111917.I1
111789.71
111661.07
111134.60
111407.30
111180.16
111113.18
111016.37
110899.71
110773.13
110646.91
110110.71
110394.76
iioi68à93
Log.Sin. I Log.Tan.
9.9117^"
9.9117181
9'9Si66Si
9.9116010
9.9$ m99
5?.^1I4717
9.91 141 14
9-9UU9t
9.9111818
9.9111114
9.9$ fis 90
9f9St09S6
9.9110310
9.9109681
9.9109049
9.9108411
9.9S0777S
9.9107138
9.9106100
9.9I0I861
9.9701113
9-^704583
9.9103944
9.9I03303
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9.9101011
9.9701380
9.9100738
9.9100091
9.9499471
9.94^8809
0.3.011^37
0.30x9474
0.301631^,
0.3013113
0.3009994
0.30068361
0.3003680
0.3000716
0.199737»
0.1994110
0.1991070
0.1987910
0.198161^
0.1978481
0.1977337
0.19711^
0.1969074
0.1967^4
0.196177J?
oa97963^8
0.1976703
o;i9733^«
o.i9foi3i
0.194710^
0.1943^^
0.1940844
0.193771^
o.i934f^
0.1931467
0.1918341
•■^kirfh«*«M
6
17 Grad
1 1
Xi
» 6
7
8
9
10
IJ
II
ÏÏ
14
IJ
17
zo
21
M
if
»7
Z9
10
Sinus
■>. - . ».
4ÎJi?^*of
4f4M-^7
4f4J0.88
4547^.7^
45fe».6^
4fji8.59
4m449
4ff8o.38
4féo6a7.
4f6$i;i6
4f^f8.04
45^83-^*
/IS709'79
4S76i.S^
4^787.3^
4f8i3.iir
4583^.10
4S^^9S
4f8^.8o
4fP4Z^8
45:9^8.32
4f5>94'if
46019.98
4^4^.80
46071 .6z
46097^4
46123.2^
46149*06
46174.86
Tang>
Î09îz.f4
J0989.19
fiozf.Sy
^lOél.^Z
I I !■■ M
S 1099.19
5:ii3f'88
fii7M9
5:1x0^.30
f 1146 «01
rii8i.7f
fi3iMo
S139SM
514X9.80
51466.58
5I5OJ.38
5I540'I9
51577.01
51613.85
51650.69
5i687.5f
5i7>4«4i
51761.19
5x7^8.18
5^835^8
51871.99
51908^1
5I94T^4
51981.7^
51019.74
5*056.70
Secans
I1Z3Z.6Z
I1149.16
11165.9%
11181.59
11199.18
11315.98
11331.6^
11349.41
X1366.16
11381.^1
l^i99.69
11416.48
11433.18
11450*10
11466^3
11483.77
ii5oo«63
11517.50
11534-3^
11551.19
11568.IX
11585.14
11601.0^
11619.05
11636.03
^11653 .01
X1670.03
11687.05
11704.08
11711.13
11738.19
Ljtjg.Sin»
9.6570468
9.657194^
9.65754^3
9.6577898
9.6590371
9.658^841
9.6585311
9.6587780
9.659014^
^*659l7l<>
9.6595173
9.65^634
9.6600093
9.660x550.
9.6605005
9'66o74S9
9.6609911
9.66x1361
9.6614810
- f ' ■ Il » n -^
9.66I7157
9*66x51701
9.6611145
9.6614586
9.6617016
9.6619464
9.6631900
9^6$4^$S
9*66^676^
9^6$9i99
9.66^6li%
9M4^6
9*707l6S9
9.70747fe
9.7077901
9*7081011
9.7084141
9.7087158
^7090374
- — — ■ — ^ '
9.7093488
9.7096601
9.7099713
9.7x01814
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9.7x09041
i r: ,».
9.7X11148
9.71X5154
9.71X8^58
■■ ■ w
9.7X1X46X
9.7x14561
9.7x17661
9.>l3076l
9.7x3385^
9.7x369^6
9.7x40051
9-7î43i4f
9«7X4^i37
9.714^»^.
9.71514X9
9'715SSC»
9.7^f8W
9.7x61681
9.71^47^7
^
fg
60
S9
58
S7
SI
11
51
50
f
47
4^
41
44
43
4»
41
40
îf
58
37
11
iS
34
33
3»
31
30
^z Grad
Sinus
8^987.44
S^74ai
8^éi.oo
89047-77
8^034.f3
8^^i .XrS
8^008.0:^
8895^4.7^
88^8.»!
88yf4-P3
88j>4i.^4
88^28.34
88pif.o|
88^x.7*
8888B.3P
8887f^
88851.7»
88848.37
888|f^»
fô8>i.é5
j 8^808.2^
^78M4
887^5.15
8Ç7f4-75
88741 .14
887*7.93
887Ï4.T1
88701 .08
Tang^
96z6i.o%
9S979*io
95838.37
9SSS7^}9
^54x7.13
^^277.04
5>5i37ii
9^997^1
^4857.71
94718.26
94578.96
94439.81
5?43oo.83
94162.00
94013-33
93884.81
9}7^.^5
93 ^«•*5
9347Q.20
9333 *-3ï
^Jî3i94.57
Î9305<J^8
91919^56
9i78*.28
-^2645.16
9*5o?.i9
92371.38
92234.72
920^8.21
Secâns
220268.93
■ ■■ ■ ■ I ■■! ^ »
220143.^6
2*0017.7^
21989^.49
%197^'U
21P642J9
119517.33
219391.62
219268.08
21^143.70
119019.47
2i889Jufi
218771.50
218647.75
218524.17
218400.74
11827746
2181^4.35
21S011.351
*X7908.55»
21778^.^4
21766346
U754l»i2
M74i?^5
*I719^^
*^7Qfi^S
^t^93t.8Q
^X68I94Q
*I6689.I5
2J6568.06
1
Lûg^Sin.
9'9^9lè09
9»9^^t6S
9^9WS^i
9-9496876
9'9A96H0
9.9495585
9.9494938
9.9A9^z9t
9'9493Hf
9.9491997
9*9^^1^
9.9491700
9.9491051
^.^90402
9.9489751
9.9489101
9.9488450
9^9^799
9.9A^7H7
9.94^649^
9.9485842
9.9485189
9^484535
9.9483881
9.9483227
^.9481571
^^481916
9^9481260
9.9480604
9^94799^7
9.9479289
Log.Taff.
IO.292834I
10^925219
10.2922098
10^918978
10.291^85^
10.2912742
10.2909626
10.290^512
10.29033^9
10.2900287
10.2897176
10.2894067
10.2890959
10^887852
10.2884746
xo.2;88i64X
- —
10.287853P
10.2875438
10^872338
10.2869239
X0.2866141
10.2S63044
10.2859949
10.2856855
10.28537^3
ioa8$o67X
10.28475 8x
XO.2844492
10.284140^
10.2838318
10^83^231
•«H
»«•
83
E
32-
33
3J
Je
40
41
43
44
46
47
48
49
Si
7î
J3
!j
SS
$6
ÎI
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2.7 Grad.
Sinus
45174.86
46200.^^6
461x6,46
4615:1.1$'
46178.04
46303.81
46319.60
4635:^.38
46381.1^
46406.91
46431.69
464^8.4^
46484.11
46^09.96
46^35.71
^6s6ï.i^S
4^^87.19
46611.93
46638.66
46664.39
46690.11
4671^.84
46741-16
46791.98
46818.69
46844.39
46870.09
510^6.70
y 1093 .68
5:1130.67
^1167 .67
^1104.68
5:1141.70
5:1178.74
^131^.78
f*3f»-84
J1389.9®
4689^.78
4^911*47
46947.16
f 1416 .98
5:1464.07
fijox.17
^1^38.19
fiy7y.4l
^1611.5:4
^1649.69
fi686.85
^1714.01
5'i76i.io
Ti75?8.39
1183^.5:9
^1871.81
5fi9io.04
fi947.i7
J1984.ÎI
53011.78
J30J9.06
5:3096.34
13133-64
IÎ3170.94
Secans
11*738.19
»7ffJ^7
177*.37
1789.48
z8o6.6o
1813.74
1840.89
185:8.06
187^.14
1891.44
i909.6y
1926.88
1944.11
»p6i.37
Z97^i
199T.93
3013.13
3030.^1
3047.88
^o6f.ii
3081.58
3099.^6
3"7.3r
3134.71
3151.17
3169.61
3187.06
3104.52
3111.00
3139.10
3257^1
^9.6644056
9.6646481
^.6648906
9.6651319
9.6656168
9-6658586
9«^66iooi
9'666^^iS
9.6665818
9-6668138
9.6670647
9.6673054
9'667S^19
9.6677863
9.6680165
9»66îi66s
9.6685064
9.6687461
9^6689iÎ6
9.6691150
9.6694641
9.6697031
9.6699^0
9.6701807
9.670419»
9.6706S76
9.6708918
9.6711338
9.6713716
9.6716093
Log.Tan
9*716^767
^.71678^1
9*7170931
9.7I74OI4
9-7177094
9.7I8OI75
9.7183151
9.7186327
9.7l^9¥>*
9^7191^76
9.7I5>114^
9.71^8610
9.7201690
9.7204759
9.72078*7
9.7210893
9.7213918
9.7217012
9.7220085
9.7223147
9.7216107
9.7229266
9.7232314
9.7235381
9.7238436
9.7*41490
9.7144143
P.7247Î91^
9.7150646
9.7213691
9.72I6744
«iM»
l
1*7
^2. Grad.
Sinus
88701 .08
88687.64
88674.-2)0
88660.75:
26 88647 .ii>
2f 88633.85
14 88610.36^
zj ' 88606.88
ul88fi93.3p
11 88^7^.8^
%o'88f66.j^
i« 88^3^.36
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16017.91
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161416.91
61366.48
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61185.49
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63^065.13
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47
46
4S
44
43
4%
41
40
3»
37
3^
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34
33
3*
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75;470.5^ njo^é.84
7f4rx.S7
7f4^>.78
7S4i$M
7S394*S7
7f 371-46
71316.34
7i337.ii
713iko8
71»98.^4
7f%ép»^^
7fi4M9
7li»».33
75103 a ^
7^83*^8
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mk"
71X64.80
75141 «61
75X&6.4I
75i07ax
75988,00
75o68.7^
71P49-17
75030.34
7f«X.XX
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74^1.87
74^7».6»
74^r*37
7493 44X
74fS4-84
748sK»l7
4766.87
46^MP
14^32.15
4^6^18
4f«>x.76
4834*^^
4164.8^
44^7.61
4430-41
436346
4*^6.15
4ft&^.o8
4S Grad.
Secans
l»4il-3x
4x62.0e
40^5.08
4018.15
3f6x.i6
38^4.41
38x7.6x
3766.85
36^4.14
36*7.47
3560.85
34^4.»7
34>7-73
3361.14
3*^4«7^
31x8.3^
3x62«03
3«95.7X
3<^9*44
1*374.33
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5»i7*.lo
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5M70.87
5t1to.11
5io6^w|i
5101S.76
51^8.15
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51867.08
51816.61
51766.1^
5I7T5.8X
5166548
5i6lf.lO
51564.^6
515x4.77
5x464.61
5x4x4*5*
5x364.47
5x3x4.46
5X164.50
5l«4.ff
5XX64.71
5x114.8^
5 1065 .XI
51015^38
S^96S.69
S09a^jO$
9-^770096
9.^69993
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9j^777799
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9.877560X
5'.87745'oi
^.8773401
^.8771300
^.87711^8
10.06083 é^
10.060^ 81B
10.0603167
10.0600716
10.05^8165
io.o5pjr6if
10.05^3064
10.0590514
10.0587^4
10.0585415
10.0581865
10.0580316
xo.05777^
10.0575118
10.0571^
1Ô.057011Ï
^.87667%
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9.8764^74
^.8763468
9.8761361
f. 8761 153
9.8760145
9.87^9036
9.8757^*7 rxo.o56i47l5
1 "■
10.056757^
10.05650x4
9.87568x6 j io.ô5595«
9.8755706 io.o557jrt
9.87545P4
9.875348»
9*%7m69
9,8751156
9^8750142
9.8749017
9.8747911
9.874675>5
9'^74Sé79
9.8744561
io.0f5ii8i!J
10^54973 P
10.0547193
10.0544646
10,0542100
10.05395^ 53
10.0537007 -
10.05 3446x|
10.0531916I
1
J 11^
12
33
34
!f
37
!f
41
4*
43
44
11
47
R
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41 Grad
— — ^
, Sinus
— I *
66i6z.oi
66^oS.S7
6^317.34
■T"*^
•66$70.Î7
^^414.37
6643^^.11
^^4f7.8T
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S847M3
$8^14*49
885:76,30
8S6^8.u
88é8Q.i7
8873 *,if
88784.16
8883^.10
8888t,^
885>40t34
6647^.59 '88p^i.4f
66^2.3.04
■^T
8^44.^^
8yop6,7f
S^i4S.P4
9çi^17*99
8941041
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66SH»7S
6éî98.i7i8^i5''3.4i
66éoy.87
4667^ ^946tM
66696.61 \9^SiS, 06
6^71 8.18 189^^747
667^9.94 ' ^96x9*91
89^7^48
89714*87
89777.3^
89819.94
8988l.fl
8993f.ri
89987.7^
90040.41
46761^
y4t^^783.i<$
66804.91
668î6.rf
6^848.18
66869.81
66891*44
66913.06
Secans
33yi^-M
3968.41
4003.17
}i0^7^91
3588.03
^6tz,46
$6s6.9i
3 691 «41
37M-^4
37^049
Î7^ft97
3819*^8
3864.31
3898.^^
3^3-^^
4^1.76
4107.61
4^4»*48
4177^8
4WV31
4*47.»8
4181^17
4317.*^
43<:i;34
43^7.4»
44ii»f3
44Î7.^7
449»-8^
4f 18.04
4f^3-»7
9'8ili646
9.8*f4073
9.8liffoo
9Szté9%6
9.8118351
9.8M977J
9.81^1198
ir.8ui6ii
9.^14641
9.8115463
9^8116883
9.8118302
9,8u97ii
9«8i|ii38
9.8i3if5^
9.8133971
9-8135386
9.8136800
9.8138113
9^813 9616
9.814^437
9.8141448
9.8143858
9.8l45î6t
9.8146676
9.8148083
9.8149490
9.81^0896
Il I ■ y
9*8ifi3or
9.9153705
9.8iffl99
9.94^8084
9.9470630
^^473 I7f
P*^47f7»o
9*9478i6î
9.94808K»
9'94^n^f
9*94^S%99
A9488443
9.94909^7
9.9493^31
9.94^6o7f
9.9498619
9^9foii6l
9^9fo$7àf
9k9îé6%4%
'S^9fàZ79t
9i9fïî 334
9.9iii^i^
9.9^16419
9>9fi^96t
9.9f^fSof
9*9f%4<^4f
9.9^i6sn7
9^i9i%9
9.PTjr^70
959534»» I
9*9%^é7%%
9^9^^9X^
5«.^T4ï854
9^443?5*
■••-*■
■■b
I
I
48 Grad.
z6
il
i4
H
*z
II
70
i9
iS
17
lé
If
II
II
10
9
1
7
7
4
I
Sinus
748^ -f 7
7487^.25^
748f7.oi
74857.7»
74818^41
747P9.ii
74775^.81
74760,4^
74741.17
74711.84
74701.^1
74^3-17
746^3.81
74^44.4^!
74^25 .10
74^.74
74f«^.J7
7M^é.99
74s ^7 '60
74iri8.it^
74fo8.«i
744*^^40
74469*99
744fo;57
744?î*iy
744ÏIV7»
743^.i^
7437».«f
745t3'40
743^3-94
7431^.48
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1301^.44
,1 '
11^^3.11
ii8p7.oz
U830.88
1136^.09
il' 2303 .19
12237.^-4
12764.78
11698.72
11631.71
Iif66.74
ii^èe.8i
»434'-^3
11171.83
»io6.i6
11040.53
ii974'9S
u 909*41
11843.91
11778.46
1 1713.05'
11647.68
11581.3$^
11517.06
Ii4fi.8i
11386.61
J1311.46
iiif6.3f
Secans
50916,05
50866,45
50816.90
S<yj67.S9
111^1.17
11116.14
11061.15
50717.93
50668J51
50619.15
50569.81
50510.54
50471.31
50411. ïi
503^1.97
50313.87
50174.81
50115.80
5Ô176.83
50117.91
50079.03
150030.10
49981.41
4993 »i^
4988J.97
4^83î-3ï
49786,70
4^^38.13
49689^1
49641.13
49591.70-
49144-3^
4949S'9^
49447'^S
Log.Sin,
9.8744561
^•8743443
9.8742315
9.8741105
9.8740085
9-8738965
9.8737844
9.8736722
9-^73SS99
9.8734476
9.8733351
9.8731227
9.8731 102
9.8729976
9.8728849
9.8717712
9.8716594
9.8715466
9.8714337
9,8723207
^,8721076
9.871094^
9.8719813,
9.871 8681
9.87175^48
9.8716414
9'^^U79
9.8714144
9.87i3ob8
9.871 1871
5.87x0735
LogXan.
»— I— — — ^— i— •
10.053191^
[ 0.05 193 70
[0,0516815
[0,0514180
10^0511735
L0.0519190
[ 0.05 16645
[O.O5I4IOX
10,0511557
[O.Ô5 09013
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[O.O5O39I5
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[O.O498838
[O.O496I95
to.04937jri
[0.0491109
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rO.0483581
rO.0481039
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10.0473413
ro.047o87i
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1 0.0465 785
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[ 0.0460707
ro.0458166
10,045561^
il
l
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7
8
9
lo
II
Î4
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17
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■ ' ' ^ ■■ I»»
65^13.06^004041
66^3 4.67 jpoop3,o^
66^)6^8,^014;. 80
66^/7.88 5'oi^8.y4
41 Grad.
Secans 1 \Log.Sin.
665i?9 «48
6701 1,07
67041^66
670^4.14
^708 J, 8 1
67107.3P
^7l*?.9f
67ilQ.f1
67X7if06
671^3 .61
67Zi6.6%
^717^.73
5730 i.xf
^7344*^7
^73^5.77
9oifi.3i
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90^9*79
90461^7
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90780.Î3
^0833.60
90886.7J
^^39.84
5»opp3.oo
91046.1^
pioyp.41
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1545:63.17
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i34^33'8*
13466^.14
1547044^
13473^-87
13477^-*^
1348x0.71
134846.1^
13 4881 .6^
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675r16.1i} Pif 2^.1 f
^S1747 \9l^79'^%
^f5>.oij 91633.1»
134^17.^1
i3495a-?^7
134988.3^
I3r5>*3-i>8
13W9.63
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13^16^76
13^101.5:4
13^*38.^
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13^381^86
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9*8163 fil
9.8164910
94*66307
p.8167703
9.8169098
9.S170493
9.8171887
9.8173179
9.817467I
9.817^3
9.8i774f3
9.81788^
9.8180131
9.8181619
9*8183006
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9.81 8f 77(8
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9.8i88f47
9,9f 44374
9.9^4^915
9.9f 494^1
9*9$S199%
9.9ff4«$
9^S707S
9*9SS96ii
9-9^6ilf4
9-9^64694
9.9f67»3^
9'9$6977%
9,95 7^Jlt
9*9S74^S^
9-957738^
9^f799i7
9*95 8146;
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9^f87f4»
9-9590080
9.ff9»6i8
9*9S91iSf
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9i8i8993<) 9>96o784i
9.81913 II
9*8191694
9.8194075
9.8i9f4f4
949610378
9i^6»9X5
9^x5451
9.9617988
9»8i96%J l9^9^A05a^
£7
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74i7T.f4
74*T^'0^
'74*5^-ï7
74217.08
741^7^8
f3
Ji
f
47
¥
44
4t
40
!f
37
34
33
3*
31
47 Grad.
Sinus
■ ■ S'
74314^8
74I7S.08
74lf8.f7
74i3î>-<>y
741 IM3
74100.00
74080.4^
740éo.pz
74041.37
74OM .81
74001^^^
75981.^8
7396^ M
739^3 -9^
739044 f
73884*7^
738<^y.ïf
73^45*^4
738if.5>i
738o6*zp
7378^.^6
■* ■■
737^7.0*
73747.38
737*7.73
Tang.
fc— — .11 n
1110^1.25'
11^,6.30
H0^31.40
no86é.y3
ji 0801 .71
11073^.93
I {0^71.15!
Uoéo/.fo
110541.84
X 10478.13
110413.^5
110349.11
110184.^3
IXOUrO^iy
ÏIOIfy.78
X 10091 41
110017.09
xo996i.8i
I09898.fé
109834.36
109770:10
109706.08
109641.01
io^T77.97
^09SJ3*97
1094^0.01
109386.16
109311.13
109158.40
l09X94*6o
XO9I3O.85
Seçatis
149447,65
49399.40
^93Si.iZ
493c^.oi
49if4-88
491046.80
4^if8.7f
49110.76
49061,80
49014.89
^8967.03
4891^10
48871.41
48813.69
48775.^^
487*8.34
48680.73
48633.17
48585 .6r
48^8.17
48490.73
48443-34
4^391 '99
48348.68
48301.41
48154.IÛ
48107.01
4815^.88
48x11.78
48065.73
48oi9,7i
Log*Sin,
9.87x0735
9^^919.7
9.8708458
9.8707319
9.8706179
9-8705<^^
9.8703898
9.8701756
9^870x6x3
9.8700470
9.86995*6
9.8698x81
9.8697037
9M9S%9X
9.8^94744
9M93i97
9.869*445?
9.8691301
9.86901 Ji
9.8689001
9.868785' I
9.8686700
9.8685:548
9.8684396
9.8683241
9.8681QS8
9.8680934
9M79779
9.8678613
9.8677466
9.8676309
Lag.Tan^
xo.e4ff6i6
0.0453085
0.04^0^45
0.044800^
00445465
0.0441915 j
0,0440385 ;
0.0437846 I
0.94353061
0.0431767
0/>4pllt;
0.04176891
0.04151^0!
0.041161 1
0.0410073
0.04175:35
O.O4T4996 1
0.04114^81
6.0409910!
0.0407^81 ;
0.0404845:
O.O4OZ307
0.0399770
0.0397233
o^3«?4';95
0.0391558
0^0389021
10.0387085
0.03 845^48
0.0381011
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$2
34
3Î
!f
37
3«
4P
41
4*
43
44
4f
4^
47
4»
4P
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3
4
S
6
7
8
9
6o
41
Grad.
Sinus
675:80.46
67601.^
^7613.33
676^.76
67666.1%
67617.60
67709.01
6773^-41
677fi.8i
67773 'iO
6779^*^9
6781 ^97
67837.34
67818.71
67880.07
Tang.
9I633.IZ
916^6.6$
pi 740.10
91793 '79
pi 847.40
91P01.04
9W4.71
91008.4:
92062.14
9Xlif.90
92169.68
92x23.^0
92277.34
9233l;2i
9238^.11
92439.0^
67901 .43 '92493 .01
67922.78
67944-Ï3
925;47.oo
92601.01
926^^.06
92709.14
92763.14-
6796s '47
67986.81
68008.14
68019.4^! 92817.38
68010.781^1871.5:4
68671.09 92921.73
68093.39 pip7^.p^
68114.69^^034.11
^8131.99 93088.49
68x17.28 93141.80
68178.I6 93197.14
681^.84 93^11.11
Sccans
131634.17
35670.34
31706.14
31741.77
3T779.03
3^811.31
3^811.64
31888.00
31914.3.8
31960.80
SS997-^S
36035.71
36070.13
36106.77
36143.34
36î79'9S
36116.18
36113.14
36189.94
36316.67
36363.43
36400^1
36437.04
3^473.89
36110.78
3^147.70
36184.64
36611.61
36618.63
3669$ J67
ié7^7S
9.83119IO' 9.9648416
9.8313310 9'96S09Si
9.8196833
Il » . ^
9.8198111
9.8199189
9.8300966
9.8301341
9.83037*7
9.8301091
9.8306464
9.83078J7
9.8309109
9.8310180
9«83i4688
9.8316016
9.8317423
9:8318789
9.8310111
9.8311519
9.8311883
9.8314146
9.8311609
■ I»
9.8316970
9.8318331
9.8319691
9.8331010
9.8331408
9.8333766
9.8331111
9.8336478
P.8337833
Log.Tan
9.9610111
9.9613061
9'96zri97 \
9.9618133
« i»^— »^—
9*9630669
9^963S^o^
9.9^35^740
9*9632z7S
9.9640811
9.9643346
9.9641 88x
9.9^53486
9.9616010
9.9^18111
9.9661089
9*966i6%3
9.9666157
9>9^^9^
9.9671221
9S6737S9
9.9676293
9.9678827
9.9^81360
9.9683893
9,9686417
9.9688960
, ■— i»"
9-96914^
9.96^4016
9i969^S9
1
i
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5o^ 737»7»73
»^; 73708,08
x8j 73688.4^
3t7|73^^8^
..M 73609 '71
*3 1 73y^.ox
X» 735^70.3»
73J^^cfaîi
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18
17
lé
If
M
ï3
II
II
10
"i
7
7
4
I
73^30.^
73511-18
73 4^1 .4^
73471.73
7345^1-^
^43*^îr
734".ro
7339*'7S
7)l7t'99
47 Grad.
Tang. I Secans
10830^.73
108241.^4
10817^.3^
733^3-*»
73335 -4^
^313-^7
73i5t3.88
73x74-09
7W4'^9
73*34-48
73x14.67
73iJ?4-«T
73175.03
73155^.10
73135.37
109130.85
109067 .14
109003.47
108939.8 3
108876.24
108811.69
108749.18
iq868f.7i
10862X.28
108558.89
108495.54
108431.23
108368.96
It>8xi6.28
108053.21
107990.18
107927.1 Ç
107864.23
107801.32
— Il
107738.44
107675.^1
107612.82
107^^0.06
107487-54
107424.67
107362.05
J07299.43
1107236.87
48018.72
47^71.76
47924.83
47877.5>5
47831.11
47784.31
47737.55
47690.84
47644.17
475P7.54
47S$o.9S
47f04.^
47457.^
47411.44
47365.01
473 1 8.64
47272.30
47226.00
4717^.75
47133-^3
47087.36
47041.23
46995.14
46949.10
46903.09
46B57.13
4681 I.XO
Vf6765.3»
46719.4^^
46673.68
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